Acronyms:

BT/Bandage = Bandage Toss
Curse/Ult = Curse of the Sad Mummy

Amumu is a very powerful tank and can be amazing. Many people overlook Amumu and continue to play other tanks.

If your enemies are terrible and cant kill you no matter what. You could change up your banshee's veil with something a bit more powerful.

The Sunfire Cape is really helpful with its passive 35 damage to enemies. However you could change it out with a Frozen Heart for a bit more armor.

Another item you may want to consider adding is Thornmail if its a high Attack Damage team.

Mercury's Treads can be replaced with Ninja Tabi for the armor and dodge.

The runes I added will greatly increase your health and all of your Regeneration.

You can add any runes you want I'm not forcing you to get the extra Hp and Regeneration.

I have played against Amumu's that use Penetration runes. I don't believe the rune slots are used to their full potential.

Flash is a very common and useful spell among all champions. It comes in handy when you need a quick escape, or when chasing down an enemy.

I use ignite because in early game I usually find myself chasing someone that's about to run behind a turret. The enemy usually has about 30 hp or under. If i pop an ignite their most likely going to die. Champions that can heal as one of their skills will most likely avoid this spell.

Pros:

Bandage Toss (BT) can be used to grab running enemies. The additional stun effect can make it deadly for players that overextend.

Despair can be a great weapon to have on when you use your stuns. If they're in range pull it out for some extra damage.

Cons:

Watch out! Bandage toss can put you into some bad situations when surrounded. Be careful what you fly into, it might hurt.

Despair can consume your mp if left on. Watch the mp or you might be dead before you know it.