Why Amumu has highest Win Rate, and low Ban Rate.
Amumu's passive, Cursed Touch, makes ganking mid devastating. His basic attacks lower enemy Magic Resistance. Initiate with Q, Bandage Toss, and smack them on the head and your ally gets a big upper hand. Additionally, your W (Despair) will whittle down the enemy's health while you chase. In team fights, Amumu can engage from a distance- jump in with Bandage Toss and immobilize the entire enemy team with his ultimate, Curse of the Sad Mummy. Once the enemy team is immobilized, with some focus your team can eliminate the enemies quickly.
I think Amumu is an unpopular choice for bans because A- Their are stronger team carries and B- He isn't perceived as the threat he truly is.
I never thought you'd pick me. 
<_-- Like this jerk.
One of a few champions that lower enemy MR naturally, the other being Ryze E.
A stun that gapcloses
Small Aoe %hp damage
Reduces the auto attack AD damage he takes with Tantrum
which allows him to be quite freaken strong.