Let's make some assumptions about jungle Amumu:
- requires blue for an efficient jungle start
- can gank at lvl 2
- builds defensive and AP items
- deals primarily magic damage
The first option (as you mentioned) is to steal Amumu's blue. Amumu relies heavily on tantrum to clear his jungle quickly, but this can quickly consume his mana. This prevents him from ganking and drastically slows his early jungle. (note: With jungle camps now providing health/mana, Amumu can still manage the jungle without blue. In times long past, stealing his blue completely destroyed his first jungle clear).
The second option is to ward/counter-gank. Bandage toss gives Amumu a strong lvl 2 gank. With map awareness and a key ward, the opposing jungler can counter-gank Amumu early before he has any defensive items.
Some junglers also have strong skills when dueling Amumu. Mundo, Shyvanna, and Lee Sin will typically win duels without outside help, and these champions excel at counter-jungling him as well. This can be especially true since Amumu tends to jungle with low health early on.
As the game progresses, Amumu's ganks will rely on hitting with bandage toss. Keeping wards in common gank locations and using minions for cover minimize his chances to succeed. Purchasing MR can help, and having cleanse or a QSS help immensely with escapes. Amumu is also susceptible to silences/stuns, so a team with high CC can prevent these. Also, a Banshee's Veil is very effective vs Amumu.
Janna deserves a special mention, as her ult will directly counter Amumu's if he doesn't kill her first.
tl;dr: Amumu is a tanky jungler and great initiator. He can be shutdown the same as other junglers via counter-jungling and early invades. His strength comes through mid to late game, but if he doesn't succeed early, he'll never get there. Strong early-game junglers who constantly steal his jungle are the best counter to him.