As I'm sure you'd guess, there isn't a clear cut answer to this question and you'll likely get all sorts of different answers.
Obviously tanks are supposed to soak up damage and initiate team fights. Their job is to protect your carries who do the damage.
Each tank has their perks.
Rammus - Really fast movement speed, one of only 3 tanks with an actual taunt. Exceptional defense against AD attacks. Very good jungler, pathetic laner.
Shen - Has an AoE taunt, has damage soaking shield, and a global ult that shields and teleports you to a teammate in need. Can Jungle (but more slowly than others) and he can lane decently.
Amumu - AoE ult that stuns/snares everyone nearby. Has a great initiation move. Can jungle but pathetic laner.
Udyr - Can put out decent dps, great damage soaking capability with turtle stance, great jungler but pathetic laner.
Galio - Great defense against Magic (the opposite of Rammus), an AoE taunt, decent damage, but has been hit with the nerf bat so he has a rough early game. Cannot jungle.
Alistar - His ult reduces all inc dmg by 75% making him the best damage soaker short term, has great CC if used correctly and a weak AoE heal. He cannot farm well or jungle, but he is a decent lane pusher.
Singed - Very good laning phase, has great initiation, very hard to kill/chase down. Cannot jungle.
Mundo - Decent laner/harraser. His Ult can make him extremely hard to focus down, but he is easily countered with Ignite.
Cho-gath - Extremely good laning phase and harass. His passive makes it near impossible to force him out of the lane. He's great at finishing off low hp enemies with ult, has a long duration aoe silence, and an aoe knock-up, so very good CC.
Malphite - Passive makes him very difficult to kill. Has one of the best initiation spells with his charge + aoe knock-up. Also has a decent single-target slow. He's a very good jungler and a decent laner.
I'm probably forgetting some so-so tanks but this basically covers them. They're all good in their own way. Notice the ones I said could jungle though. Every competitive team needs a jungler and some tanks are very good junglers and are otherwise very poor laning mates. There's other tanks that can't jungle but are otherwise very good in the lane.
It really just comes down to which one you find the most fun. Overall, tanks are pretty well balanced at the moment.