The greatest champions not in lane to counter Amumu include Lucian, Aphelios, and Caitlyn. These champs are all good at countering Amumu with win rates over 57%. Even if these Amumu counter picks are not chosen opposite your position, it's not smart to play him into any of these matchups. They will usually destroy Amumu.
Yet, if the opposite team brings either Heimerdinger or Kassadin, Amumu mains should seriously think about picking him, as he easily beats these champions with win rates over 55% against both ofthem.