Other than having a low item and level dependency (as mentioned here) a good roamer needs to be able to do a few things:
- Counter-jungle
- Deny the opponent's solo
- Gank
I'll talk about why each of these are important, and what champions other than Alistar fit these roles very well.
Counter-Jungling
Counter-jungling is simply screwing with the enemy jungler. Junglers are countered by stealing their buffs and denying respawn.
Stealing buffs can be crippling to many junglers, as buffs are needed for clearing the jungle faster and ganking. For example, a jungler without crowd control needs Lizard to slow when ganking. A jungler who needs their abilities to jungle effectively (Nunu/Shaco) relies heavily on Golem. Stealing either of these will not only deny the jungler experience but likely prevent them from ganking other lanes, making your allies lives easier.
Denying respawn is simply done by killing the highest experience value creep in a camp of the enemies jungle. This gives less experience to the enemy jungler and the creeps will not respawn until the jungler kills the entire camp. Good creeps to do this with are the Big Banshee, Big Wolf, Lizard, and Golem.
Keep in mind that going for enemy buffs is extremely risky; most teams will actively protect their jungler and you might mind end up in a 1v3. A roamer needs to be able to deal with this.
Denying Solo
Simply put, prevent your opponent's solos from getting experience. Running into a lane and harassing the solo enough that they have to blue pill back home is basically all that you need to do. This gives your team's solos some free time to level and get last hits without harassment.
Ganking
This largely happens along with denying solo. In order to do this a roamer needs crowd control so that your allies can get in to do damage. Even if your gank fails, as long as you manage to get the enemy champion to blue pill back home you have successfully given your allies an opportunity to freely farm their lanes.
An important thing to remember is that you do not want to get the kill from a gank, unless the target will escape without you taking the kill. It is more important for your carries to get the gold in order to carry your team late game.
The glue that keeps it together
To accomplish the above goals you need to move quickly. This usually depends on the boots you choose, but getting the gold for those boots can be difficult as a roamer, so inherent speed is important.
The less time you spend getting from lane to lane the less experience you will lose while traveling. Although this isn't a huge deal, because you losing experience means your allies are gaining more, you still need to be able to travel quickly in order to take advantage of opportunities when they present themselves. Fast traveling means you can run to the enemy jungler when you see him at the buff you warded, run to a lane to gank, or escape from a nasty scenario where the enemy team decides they don't like you roaming.
Alternatives to Alistar
Addressing all of the above roles, I have a few champions suggestion other than Alistar.
As stated in other answers, a champion who can jungle tends to make a good roamer, because both roamers and junglers have similar roles (deny solo, gank, counter-jungle).
Nunu in particular is a great roamer because of his abilities. Consume is a natural Smite, ideal for stealing buffs. My games usually start with me warding the enemy Lizard or Golem (depending on the enemy jungler), and waiting until they bring the creep down low so I can flash in and Consume. If that proves too risky I waltz to the banshees and consume Big Banshee for an easy respawn denial. Blood Boil is a great way to get around the map quickly, especially with Boots of Mobility. Less time traveling means you lose less experience and get more opportunities to be present for a gank or push. You can also cast on an ally to make them even deadlier during a gank while still getting the advantage for yourself. Ice Blast is a wicked ganking tool, providing a massive slow that is a nice lead into the ultimate Absolute Zero. The combo should give your allies plenty of time to run in and take out the target, but be careful not to take the kill with Absolute Zero's high damage.
Evelynn also makes a good roamer. Her ganking is ridiculous, and I won't bother going over how it works. Instead of stealing buffs, unless you have Smite, she tends to be more effective at scaring off junglers when they try to take a buff. Especially at level 1, many junglers get very low hp while taking Golem or Lizard. It's an ideal time to kill them with a stun/Ignite, or at least scare them off. If you take an Ignite/Smite combo you might get both a kill and a buff (win!). Going invisible makes Evelynn impossible to catch early game unless someone invests in an invisible detection wards (which will not happen), so there's little risk to counter-jungling. Her ultimate provides a massive speed boost around mid game, making her a very fast traveler, especially with Boots of Mobility.
There are plenty more roamers that I won't care to mention but given the criteria it should be easy to point out which of your favorite champions can make a good roamer.
Riot games have put a special effort into having balanced champions for this game style as well. I don't believe there are any champions to avoid. However, the team composition changes a bit.
AP Carry
You will still need one, or else the other team will just build against AD and will own you as soon as they are a bit stuffed.
Tank / Off Tank
King in solo holding the bot lane, also very good in "tower diving" (if we can still call it so in Dominion).
Melee Fighters
They tend to be the heroes everyone picks as they are sort of kings on this map. They deal quite some damage and have high sustainability (so they don't need to Back often), and are often very good in 1v1 (which happens pretty often in Dominion).
Ranged AD Carry
More than one is too much, but not having one (to have more fighters) is a handicap. He deals crazy damage and can attack out of tower range or defend minion waves without exposing himself in front of the tower. From the games I've played or seen, having only melee champs is clearly a handicap.
Support
I rarely see them in Dominion and believe they are overlooked. Each time I've had one on my team, it was awesome to hold the windmill (we never had to back, support would always buff/heal us).
However, having a support requires good team play, because the champion won't do anything on its own (compared to fighters).
General
As XP gain is so fast in Dominion, teams are usually built with mid/late game champions. Riot tried to correct this in a previous patch by lowering the XP gain aura on the map, however, you still get to level 6 tremendously fast, so don't hesitate in taking weak early game champs (like Kassadin, useless before level 6).
Try having a hero or 2 (at least) with high mobility (Rammus, Kassadin, Nocturne, Twisted Fate, etc.) to do lane swaps and be unpredictable in your tower attacks.
Conclusion
All heroes are viable. It all depends on the team composition.
Good Akali, Irelia and Xin Zhao champions can however be freaking awesome with their ganking abilities and life steal.
Best Answer
I don't consider Nasus a true tank - he has no real Tank abilities, and serves better as a Tanky DPS / Anti-carry. That said, here's a list of the heroes I consider true tanks in the current metagame.
Alistar
I'll grant you that Alistar's hard to play optimally, but when he is, the bull's a force to be reckoned with. Two hard CCs (neither affected by Merc Treads). Triumphant Roar makes him an excellent pusher, and his Ultimate and high base health make you an excellent damage soak. Additionally, little of his power comes from items; Pulverize + Headbutt is really good even without any bonus from AP.
Amumu
Amumu's got two major things going for him: He's a great initiator, and he's a tank who can jungle and gank effectively. Due to the experience bonus, most top teams have a jungler on Summoner's Rift, and Amumu's one of the better ones. He also has two hard CCs in bandage toss and his ult, which can make escaping from him quite difficult (not to mention keeping folks within Despair for longer)
Cho'gath
Poor Cho just get nerfed pretty bad in the Nocturne patch, losing substantial damage numbers from feast. That aside, he still is a decent (if not a first pick) tank with a skill shot initiation ability (though Rupture is more easily dodge-able than some other initiators) and an AoE silence. There's also something to be said for the psychological and mechanical effects of having the largest model on the screen. You'll be shielding your allies from attacks simply because your opponents can't find them to click under a fully-feasted Cho'gath. After you've maxed your feast stacks, try using Feast earlier in fights rather than later: it does true damage, and it's a pretty sizeable nuke - carries especially tend to panic when 1/4 of their health (or more) suddenly vanishes.
Galio
Mana-regen problems aside, Galio is a strong Tank. His most notable skills are his Ult and his Gust -- an AoE taunt nuke is especially powerful when combined with other AoE ults, such as Annie, Amumu, Morgana, Malphite, etc. Gust is useful both as a chasing mechanic and to help allies escape. Unfortunately, opposite-but-otherwise-like Rammus, Galio's usefulness tends to diminish in matches with primarily physical damage where he can't make full use out of his passive.
Garen
Garen is not a "typical" Tank, and works best as an Offtank due to not having a strong initiator or CC other than his silence (which is pretty useful in and of itself). Garen's a tough character who can bring a lot of damage to a group of enemies between judgement and his iconic sunfire cape. His ult is interesting, as it can be difficult to judge when to best use it, though some players dislike it because of its tendency to "steal" kills.
Gragas
Gragas gets a damage reduction, an AoE Slow, Area Denial, and a massive radial knockback on a relatively short cooldown. He works well as a tank (consider starting with a rod of ages) because of fight disruption alone, and drunken rage and happy-time give him quite a long longevity as well, making him a passable pusher.
Malphite
Malphite joins Cho in having been hit with the nerf-bat in the last patch, but is still a strong tank. Like Amumu, Rammus, and Shen, Malphite can jungle effectively, and has a combination of an impressive initiator, and a damage-dealing skill that scales off of armor (so even building straight tank items, you can deal a hefty sum of damage). With his Q, he can be especially effective by tunnel-visioning enemy carries.
Maokai
Maokai is a great tank based around team fights. His ultimate is an AoE damage reduction, which when strategically placed, can turn the tide of fights. He has a snare, which is great to gank with, or focus down the enemy carry, a small AoE slow, and a really strong harass with his ranged sapling. His passive makes him have a very strong laning presence. After every 5 abilities, his next auto attack heals him 7% hp. This is also a incredibly useful skill in team fights, giving him huge survivability potential.
Mordekaiser
Mordekaiser can be an incredible tank, especially if he gets a few early kills and gets an item and level advantage over the other players. Though I've heard of folks jungling as Mordekaiser, I prefer to see him in a solo lane, where a good player can easily 2 v 1 by abusing Iron Man (well, perhaps less easily, depending on the opponents, but I've seen it done across a number of games). Make sure to get some AP to go with the Kaiser - Rylai's or an Abyssal Scepter and Sorc Boots make for a very offensive tank, especially in the laning phase where his short cooldowns make for an easy harass.
Nunu
When built properly, Nunu makes a great off-tank. The thing you have to realize about Nunu is that the slow on his E is insane. It's 70% I think at rank 5? If Nunu catches up to you alone, you are not getting away from him if he has the mana to continually iceball you. Also important to note is Consume - the health it restores is not insubstantial, and with a Will of the Ancients, you can easily recover half your health every 10 seconds or so.
Rammus
Rammus has everything a tank needs - a damage reduction ability (defense curl), an intiator paired with a slow (powerball), hard CC and target peeling (taunt), and team fight presence (tremors adds up fast!). Did we mention that he could jungle and his taunt has a relatively quick cooldown? A top pick for sure.
Shen
Shen is probably up in the top 3 with Amumu and Rammus when it comes to tanks (in my mind at least). If you can learn to correctly handle his Energy (which can be a little tricky to get the hang of at first), a good Shen player can be phenomenal. He's got a damage shield, an AoE Taunt, and a global ult / ally savior mechanic. One thing to note is that you don't want to build dodge on Shen - build armor/MR and health instead: it makes his passive come up more often and for more damage.
Singed
Finally, Singed. Singed is known for running really fast - make sure to take ghost, as it lets you spread your poison much more handily without having to path around enemies. As singed, you want your opponents to chase you; with your ult you're more than likely faster than them (and insanity potion lasts for an unmatched THIRTY SECONDS) and they'll kill themselves on your poison trail if they chase you for too long. Of course, when they finally break off, that's when you turn around, stick 'm with your adhesive, and then fling 'm behind you into more poison. Fling is an okay initiator, though it takes practice to make sure you're not accidentally throwing the enemies away from your team.