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.
The metagame is established generally through the thousands of games played. Usually, teams will get together and decide to try a team composition and success will lead them to keep trying it. Obviously, over just a few games everyone's performance will vary widely and no meta will save you on your bad days...
...But over thousands of games with hundreds of thousands of players, individual skill becomes averaged out and what you're left with is what strategies tend to work. Now, we need to distinguish a strategy from a meta to make a lot of sense here. I'll do it very briefly: The metagame is a framework in which you insert individual pieces (champions and builds, where builds are item/mastery/rune combos) that fit the framework. In our current state, the "meta" is usually a high-survivability (but not usually tank) in top who can solo and scales well with items and experience; mid is a character that scales best with experience; bot is a character who scales best with items and needs either baby-sitter or someone to setup kills; the jungler is highly variable, but often is prized for their ganking abilities. So, take any "pieces" that fit inside that framework, and you have a particular strategy within the meta. For instance, an AoE heavy composition is a strategy within the current meta.
Strategies are handed down from pro players (usually, but not always), but the meta is determined by all of us. It's less a "choice" that people get to make and more a mathematical optimization realized over a ridiculous number of games (millions). Metas will usually stabilize without some dramatic changes in terms of patches and champions, which is what has happened in LoL. More casual players will tend to emulate what they see the pro players do, which makes sense in terms of the number of games played per person.
Best Answer
In the current professional meta of lane swaps, you'll notice that marksmen are not always in the bot lane. I would say its even rare these days to see a normal 2v2 matchup in the bottom lane.
The reason it used be the meta to always have a marksman bot was a mixture of dragon control and needing to have a support. If marksmen didn't have supports, they would get destroyed in lane. So now we have a two man lane, but where to put them? Put them bot for dragon control to get the most of committing two people to a lane. It's not that dragon control requires a marksman, but that marksmen need a support.
Why a marksman? They fill the role of constant DPS. Without a threat of constant DPS, sustain tanks like Mundo would rule the game. Melee is poor at DPS since they have to move constantly and most AP champs are focused on burst and lack consistent DPS. The DPS a marksman brings is important both for teamfights and objectives.
As for why normal play follows this, its because the pros do it. In most games, the core meta of professional play will trickle down. Pro play is taken with a grain of salt though. An example is lane swaps or buddy jungling. These are concepts that came in response to the established meta and require coordination and communication to pull off properly. Since solo queue lacks these, the smart player sticks to the established meta. Players that blindly try to copy pro play usually get ridiculed by their team for not understanding the underlying concepts.