Does that really mean that a Wizard can be in a full-plate and be able to cast a spell with no somatic component? There's no other limit to it?

As far as a wizard wearing full plate, there would be no inhibition on spellcasting other than stilling a spell and having the necessary higher level spell slot to do it. Note however that there are other stipulations to wearing armor one is not proficient in, and there isn't a spell that I know of which grants temporary proficiency to armor specifically.

Pertinent is this rule about armor proficiency:

A character who is wearing armor with which she is not proficient applies its armor check penalty to attack rolls and to all skill checks that involve moving, including Ride.

And including concentration. Just in case you want your wizard in full plate on top of the mount.

Would still spell make the concentration check easier? Or it is already assumed that the somatic part of the spell should be considered separately? (ie: no ride roll needed but concentration stays the same)

I would rule that it would not, agreeing with KRyan's answer as far as that goes. Just like concentrating in a swarm or other distracting conditions, it seems the rule for mounted spellcasting is derived from the same. Concentration check still stands.

Abbreviations

I’ll be referring to arcane spell failure as ASF frequently. I’ll also use ACP for armor check penalty when discussing armors.

Arcane Spell Failure rules

First, the official rules on arcane spell failure, just so we’re all on the same page:

Arcane Spell Failure

Armor interferes with the gestures that a spellcaster must make to cast an arcane spell that has a somatic component. Arcane spellcasters face the possibility of arcane spell failure if they’re wearing armor. Bards can wear light armor without incurring any arcane spell failure chance for their bard spells.

Casting an Arcane Spell in Armor
A character who casts an arcane spell while wearing armor must usually make an arcane spell failure roll. The number in the Arcane Spell Failure Chance column on Table: Armor and Shields is the chance that the spell fails and is ruined. If the spell lacks a somatic component, however, it can be cast with no chance of arcane spell failure.

Shields
If a character is wearing armor and using a shield, add the two numbers together to get a single arcane spell failure chance.

The important facets here are that arcane spell failure applies only to arcane spells that have a Somatic component (though most do), and you add your armor’s ASF to your shield’s ASF to determine your total chance of failure.

How bad is Arcane Spell Failure?

You really, really do not want any ASF at all. A 5% chance to fail, no matter what you’re doing, who you’re targetting, or how good you are at the spell, is a big problem. It’s only a matter of time before you fail on a really important spell. Remember, that spell may still require a attack roll or allow the enemy a saving throw. Increasing the number of ways an action can fail multiplies¹ your odds that it will.

With that in mind, ways of avoiding ASF:

Trivial Option: Don’t be an arcanist

The trivial answer is to just not cast arcane spells. Divine spells and psionic powers can be used in armor without any penalty whatsoever, and may be a better fit for your character. But you probably wouldn’t be here if this was the answer that you wanted.

Trivial Option: Don’t wear armor

The other trivial answer. Mage armor lasts an hour per level, which means it quickly becomes fairly reliable. Luminous armor and greater luminous armor from Book of Exalted Deeds provide upgrades to mage armor.² Still not really the answer you’re looking for, most likely.

However, this really is a good answer. The abjurant champion (Complete Mage) is an excellent five-level prestige class that grants full BAB, full spellcasting, and lots of bonuses to AC-granting abjurations. Unfortunately, mage armor is bizarrely in Conjuration instead of Abjuration; apparently even the author assumed it was an Abjuration since the example character is statted with mage armor as if it were improved by abjurant champion. Ask your DM if he’ll rule that mage armor is an Abjuration; Conjuration is too good anyway. If not, shield is an abjuration (but has a sadly short duration), and luminous armor and greater luminous armor from Book of Exalted Deeds are both abjurations as well.

Best Option: Wear armor with 0% ASF

This is pretty much the “correct” answer. It’s relatively easy to get armor that has 0% arcane spell failure, and doing so is much cheaper than expending feats, class levels, or restricting yourself to a particular class.

For a shield, a mithral buckler (+1 AC, 1,015 gp) or mithral light shield (+1 AC, 1,009 gp) both have 0% ASF and 0 ACP, which means they can be used even by arcanists who do not have proficiency with shields at no penalty. Most spellcasters should pick one up at some point, as they are not expensive, and they provide a platform for special magic armor and shield properties (for examples, fortification and soulfire are perennial favorites).

The traditional answer to body armor is a +1 twilight mithral chain shirt (+5 AC, 5,500 gp). A better solution, however, is a feycraft (or githcraft) mithral caster chain shirt (+4 AC each, 2,050 gp, or 2,150 gp for githcraft instead of feycraft). Mithral chain shirts have 0 ACP, which means this is another option that can be used even by arcanists without proficiency in armor at no penalty. (Caster armor is Dragon material; if unavailable, thistledown padding from Races of the Wild can be substituted.)

For more AC, the best available is +1 twilight feycraft mithral caster full-plate with thistledown padding (+9 AC, 17,250 gp), which has 0% ASF but has an ACP, so proficiency with Medium Armor is strongly recommended.

Here’s what each option does, its source, and its cost:

• Twilight, Magic Item Compendium and Player’s Handbook II, reduces arcane spell failure by 10%. +1 equivalent, magic.

• Feycraft, Dungeon Master’s Guide II, reduces arcane spell failure by 5% among other things. 500 gp, mundane. Requires that the armorsmith be fey.

• Mithral, SRD, reduces arcane spell failure by 10% among other things. 1,000 gp for Light Armor or Shields, 9,000 gp for Heavy Armor, mundane.

• Caster, Dragon vol. 358, reduces arcane spell failure by 5%. 400 gp (light), 700 gp (medium), or 1000 gp (heavy), mundane. Requires that the armorsmith have a particular feat.

• Thistledown Padding, Races of the Wild, reduces arcane spell failure by 5% among other things. 250 gp, mundane.

If Dragon material is unavailable, there is also:

• Githcraft, Dungeon Master’s Guide II, reduces arcane spell failure by 5% among other things. 600 gp, mundane. Requires that the armorsmith be gith.

Combining feycraft and githcraft requires either a team effort by a fey armorer and a gith armorer, or some kind of weird fey-gith hybrid armorer. No rules explicitly detail how to combine these two, but no rule restricts them from being applied to the same armor either. If the combination is unavailable, a single level of Spellsword (Complete Warrior) can handle the remaining ASF for relatively low cost.

But I would strongly recommend not just allowing the combination, but making it a plot point. A great hero needs an incredible suit of armor, needs to draw upon the skills of not just a master armorer, but multiple master armorers from several completely unrelated races? That sounds like a pretty epic little side-quest. Depends on the campaign, of course.

Alternate Option: Be an arcanist that can ignore arcane spell failure

The bard, battle sorcerer, beguiler (Player’s Handbook II), dread necromancer (Heroes of Horror), duskblade (Player’s Handbook II), hexblade (Complete Warrior), spellthief (Complete Adventurer), warlock (Complete Arcane), and warmage (Complete Arcane) base classes all gain the ability to ignore ASF when wearing light armor (or heavier, in a few cases).

The shadowcaster (Tome of Magic) risks arcane spell failure on his highest-level mysteries, but at higher levels, his lower-level mysteries become spell-like abilities and then supernatural abilities, and neither of these is affected by ASF.

The Battle Caster feat (Complete Arcane) can be used to extend the ability to ignore ASF to heavier armors. This is not usually a good use of a feat, since usually you also need to take the corresponding armor proficiency feat, so you’re burning two (or four) feats for a bit more AC; this is not a good trade. Even if you have proficiency, the AC probably isn’t worth a feat. Note that you can use a mithral breastplate to get more AC, since mithral makes a breastplate Light Armor.

The Armored Mage alternative class feature (Complete Mage) for the fighter can ignore ASF for Light Armor with any one arcane class, but only for spells whose level is equal to or less than your fighter level plus 1. Pretty much awful, since the fighter levels are making your spellcasting ability suck. If you insist, a Fighter 6 can ignore ASF on light armor for spells up to 7th-level, which is the highest-level spell that a 14th-level full-caster can cast, so fighter 6/arcanist 14 is probably the optimal breakdown. Coincidentally, this is exactly how many levels the Dungeoncrasher fighter ACF (Dungeonscape) needs; there might be a weird viable build hiding in there somewhere.

Decent Option: Take a Prestige Class that allows you to cast arcane spells while wearing armor

A few options for this exist, but they usually require combination with other techniques since they often only reduce ASF rather than ignore it completely.

Runesmiths (Races of Stone) can prepare arcane spells such that they do not have somatic components. Quite good, but dwarf-only.

Urban savant (Cityscape) allows every spellcasting class you have to ignore ASF while wearing light armor. Entry requires Bardic Knowledge, or if the DM okays it, 2 ranks of Knowledge (history). Even if your DM will not okay that, he may allow Lore (from, e.g., loremaster) to qualify, so you do not have to be a bard or dip into bard to get in. They lose spellcasting at 10th level, but their capstone feature isn’t bad and you can always just not take that last level. Probably would mix well with sublime chord (Complete Arcane).

Spellsword 1 (Complete Warrior) can shave 10% off your ASF, but taking more than one level is not recommended. They do reduce the ASF more, but you also lose a ton of spellcasting.

The bladesinger (Complete Warrior), dragon devotee (Races of the Dragon), fochlucan lyrist (Complete Adventurer), geomancer (Complete Divine), pale master (Libris Mortis), and rage mage (Complete Warrior) all can reduce or ignore ASF in certain circumstances, but you cannot gain these abilities without losing spellcasting levels. As a result, they are not usually good choices if all you’re looking for is armored spellcasting.

The silver key (Dragonmarked) is a particularly poor choice, as it does not advance spellcasting at all.

Arcane hierophant (Races of the Wild) requires lost spellcasting for entry, but unlike the above options, it’s pretty good thanks to advancing both druid and arcane class features. The first level in the prestige class also allows you to ignore ASF in light armor or medium armor, provided they are not made from metal.

Knight phantom (Five Nations) is relatively difficult to get into without losing spellcasting (it requires proficiency in all martial weapons) and it also loses spellcasting at 1st. That said, it is a rather good prestige class, and ignores ASF from light armor. Probably not quite worth a lost spellcasting level and almost definitely not worth losing two, but still a decent option.

Prestige bard isn’t that good, since you lose a lot of spellcasting levels in it, but you also do get quite a few decent features, including the ability to ignore ASF from light armor while casting any arcane spell. For someone who wants to mix bardic class features with better spellcasting, sublime chord (Complete Arcane) is a much better choice, but this is definitely better than dipping the bard base class. (Sublime chord does not get to ignore ASF, so another tactic is necessary for that; urban savant above is a pretty easy option for example).

The assassin, corrupt avenger (Heroes of Horror), Ebonmar infiltrator (Cityscape), and fatemaker (Planar Handbook) can ignore ASF for light armor, the knight of the weave (Knights of Valor) gains this ability at 2nd level, and ignores medium armor too at 8th level, and the suel arcanamach (Complete Arcane) can reduce ASF by up to 15%, but all of these have their own progressions rather than advancing a base class.

As far as I am aware, that is every prestige class published that has something to say about arcane spell failure. Many thanks to the Lists of Stuff for helping me track down all of them.

Tricksy Option: Master Spellthief

Spellthieves can cast spells in light armor. Master Spellthief allows a multiclass spellthief to extend that benefit to spells from other classes. Dipping into spellthief and then spending a feat on Master Spellthief is a really inefficient way to get that benefit, and so is not a recommended approach to casting in light armor.

However, Master Spellthief also allows absurd caster level shenanigans, which can absolutely be worth the level and feat. If you’re doing that, you get lightly-armored spellcasting too.

Weird Option: Snowcasting in Blue Ice armor

Armor made from blue ice (Frostburn) allows you to ignore its ASF when you cast a spell that has the [Cold] descriptor. Normally, this isn’t that great, since there are a lot of spells without the [Cold] descriptor that you still want to cast.

However, Snowcasting (also Frostburn) can add the [Cold] descriptor to any spell you cast so long as you use a handful of snow as a material component. Since snow is free, strictly speaking, Eschew Materials means that you can ignore the snow material component and add the [Cold] descriptor to every spell without doing anything. Even if your DM injects some sanity here (and he probably should and will), if you’re in a snowy environment this might be viable.

But two feats, or a feat and accepting the risk of not having snow handy, is not really a great trade for ignoring ASF. This combination is only worthwhile if you have other bonuses to [Cold] spells: things like the Lord of the Uttercold (feat from Complete Arcane), Spell Focus (Cold), Piercing Cold, or whatever.

Note that wearing blue ice armor without Cold Resistance or Cold Endurance is a pretty bad idea, as it applies all kinds of penalties.

Niche Option: Githyanki Battlecaster

It’s a feat in Monster Manual IV, and yes, you have to be a githyanki. Allows you to ignore ASF in Light Armor. The githyanki’s LA +2 is the same as losing two spellcasting levels, so this is only a good idea if you really wanted to play a githyanki in the first place. And even then, they’re psionic creatures, just use psion instead of wizard, and never worry about ASF at all. The LA Buyoff variant can save the githyanki as an option, but only at high levels.

Bad Option: Don’t use spells with somatic components

This is purely a matter of spell selection and does not require any special investment of feats, money, or anything else. However, it drastically reduces the number of spells you can realistically use. This is not really a good idea.

Note that Still Spell can make spells lose somatic components. This is still not a great choice, since it effectively increases the spell level of most of your spells.

But also note the runesmith (Races of Stone), which effectively gets a free Still Spell on every spell he prepares as a rune.

Worst Option: Just accept arcane spell failure

This is never a good choice. The AC from the armor isn’t worth it.

That said, if you’re going to do it, your best bet is to focus on long-term buffs that you cast well before you need them. That way, if it fails, you only lose the spell slot, and have plenty of time to try again. If you have any ASF at all, you really do not want to ever cast a spell during combat or any other time-sensitive situation. Sooner or later, you’re going to fail at a point where you do not have a round to wait to try again.

Conclusion

The various armor improvements you can buy to reduce arcane spell failure leave little excuse for accepting any ASF at all, or losing spellcasting levels in order to avoid it. A mithral buckler has +1 AC, and a feycraft mithral chain shirt with either the caster quality or thistledown padding has +4 AC. Both of these items have no magic on them (which means you can put on whatever magic you like without incurring increasing quadratic costs), have 0% ASF, and +0 ACP so you don’t even need proficiency in them.

If you’re missing two of Dragon, Dungeon Master’s Guide II, or Races of the Wild available, a single level in spellsword (Complete Warrior) can replace one of them. If you have none of these, or don’t have Complete Warrior, twilight from either Magic Item Compendium or Player’s Handbook II is a more expensive option but will also work.

If you have none of these books, and are not playing a class that can naturally ignore ASF, I strongly recommend simply relying on mage armor instead of attempting to wear body armor. The mithral shield is still a good bet, though, for just about anyone.

I do not really think the +1 twilight feycraft mithral caster full-plate is worthwhile unless you can get Medium Armor Proficiency without spending a feat or losing a spellcasting level, but it is a fantastic armor.

Footnotes

1. _{“Multiplies” not being used in the strict mathematical sense; mathematically the chance of failure is \$1-\left[\left(1-P_{ASF}\right)\times\left(1-P_{non\text{-}ASF\ failure}\right)\right]\$}

2. _{As Sanctified spells, luminous armor and greater luminous armor must be prepared, not cast spontaneously, and cannot be used by Evil characters. Arcane Preparation can allow spontaneous casters to use them, however, and they do not require Spells Known since Sanctified spells are automatically available to all who are willing to make the sacrifice required to use them.}