The top picks globally to counter Amumu include Lucian, Aphelios, and Caitlyn. These champions are all good at countering Amumu with decent win rates over 57%. Even if these Amumu counter picks are not taken opposite your position, it's not smart to choose him into any of these matchups. They will usually win against Amumu.
Conversely, if the other team picks either Heimerdinger or Kassadin, you should seriously think about taking him, as he easily wins against these champions with win rates over 55% against both ofthem.