Aha! Good question. It's me! Wannabe King or Crazy 3ights. Now, back to your question. Crazy
Eights guides are all about bringing Damage to the enemy. It's almost like supporting the person carrying your team, making sure they get the pentakill. If there's no one carrying, then go absolutely Crazy and kill everyone! Be the carry!

-How do you tell if you're Crazy Eighting?
If someone on the enemy team says "[all] Joe:I hate you amumu" or "[all] Joe: Wow, fail(in ganking amumu)" or similar quotes, then you are doing great! So now that you know what it is, Let's start crying and talking about Crazy Eights Amumu!

Ahhhh, another good question. Yes, he is one of the hardest crazy eight champs, because he's not like akali or tryndamere. When they're fed its over because of their crazy DPS and turret diving. But Amumu is every passive. Instead of Blowing things up, your poisoning them. Another thing about Amumu is he's late game. It's kinda hard to be Crazy Eighting when your late game.

-Then how does he do it?!
The only advantage he has is hes a jungler. He can build up levels then gank the lanes around mid game. By doing this, if he gets fed early game and makes it to late game, then he is the most powerful Crazy eight there could be. His natural tankiness (and all the armor you build up) allows you to stop almost any bruiser 1v1 and win. Not only that, his abyssal scepter allows him to take on AP champs(not many champs are resistant to AP), melt Magic resist, and gives you ability power(It's harder to counter AP tanks like Amumu because hes AP). So their you have it. That is exactly why he can destroy the enemy team late game.

When I was buying cheap champs, I was looking for a 1350 to buy. Before I thought that Amumu was 4800, but I was sooo wrong. I bought him and now I LOVEEE HIM!(I also got the sad robot skin, too bad he gets banned so much). His abilities are awesome and hes so much fun and hes funny. Anyway, that's just the authors views on him.

Here are some tips for playing Amumu:
-Don't be the hero, you can only 2v1 late game not early game.
-Don't gank till lvl 4 (preferably lvl 6)[other guides also say the same thing].
-Don't leave despair on all the time unless you have blue buff, it drains alot of mana.

Now as I suggested, you need as much tankiness and Magic pen. as you can get. Get scaling MR(magic resist) because you usually don't see Ap champs while jungling, just ad monsters. Ability power isn't very good on him because it doesn't make much of a difference for despair. Despair rounds up from 50 for it's ap ratio, so it's not too useful. But magic pen. will affect it either way.

I go for a little Ap and some Magic Pen(we taked about the importance of magic pen. already). In the defense side I go for mostly armor and MR instead of health. But that's just my opinion, you could probably go for health just the same; as long as it's 9/21/0 it's fine.

Sunfire Cape! One of the best items on Amumu. This gives you tons of tankiness and the passive. The passive deals 40 magic damage to anyone near you. WAHZA! All of a sudden you start doing alot more damage. If you have despair on, combined with sunfire, it does a whole lot of damage. And another great thing, people don't realize that all their health is leaving. Once they do, it's usually too late.

P.S. Liandry's torment works on him because it starts to take effect while your using despair. Even though it only does 1/2 damage because it's Aoe, Crystal Scepter can fix this.

Skills are quite flexible in my opinion, but when I play him I always max despair first. This gives hima lot of early game and late game potential. 2.7% of their health each second by level 9 combined with sunfire cape. That's a whole lot of damage. I would suggest maxing bandage toss last because it doesn't help much in clearing camps, just as a utility to engage, jump over walls, and stun.

It's pretty simple what the spells are. Flash and smite. Smite is just about the best spell for a jungler(even though there are a few times i forgot smite and instead put flash revive, which also works). Flash gets you even closer to the enemy, so whenever they're just out of your despair range, you can still finish them off.

If you want you may also use exhaust for extra ganking power.

Pros:
Heavy DPS that does damage based on max health.
Has a strong passive that can melt tanks.
Nice engage/stun
Good Aoe.
High powered teamfight ult.
E Can clear jungle camps fast.
He's naturally tanky
He's not evil :P

Cons:
Doesn't have much of an escape.
Can't carry early game.
Can't do large amounts of damage at early levels.
Can be mana starved if you use too many abilities on monsters

With jungling, you have to be as quick and efficient as possible. He can easily drain too much mana. Only use your q to quickly go through walls. Only use it once on each camp.Remember, your E cooldown is reduced whenever you are hit, this applies to jungle monsters as well.

In team fights, Amumu is devastating. Sometimes, I jump in to the fight when the enemies don't expect it and you'd think "if I jump in with q they will kill me." That's usually true, but people tend to not focus the tank. So as soon as you jump in, if they start focusing you, then hopefully your team can start finishing them off. Also, your ult has a great effect on the enemy. They can't move or use basic attacks. This provides your carries to get a heads up on their carries and bruisers. And that whole time they take damage from despair.
Good Amumu ult combos:

Galio/Amumu (Galio can idol then Amumu can use his ult, allowing your team to take free shots on the enemy)

Amumu/Nunu (Amumu locks em' in and nunu ends them, simple as that)

Amumu/Maokai (This allows your team to take very little damage over a few seconds)

He has alot of unique moves!
Cursed Touch melts magic resist like crazy, giving him alot more damage with his abilities.

Bandage toss is one of the only abilities that dashes and CC's at the same time (another one is Maokai, who is also a jungler).

Despair is one of the only toggle on Aoe effects in the game. The only other one that I've seen do this is Karthus, however, Amumu's is based on health and only uses 8 mana at max level; while Karthus uses 78.

Tantrum is a great Aoe ability, and has a great passive. He takes reduced damage and has reduced cooldown on this ability whenever he is hit. This gives him strong jungling capabilities.

Curse of the sad mummy, a very powerful move was a unique type of CC. Entangle stops movement and basic attacks, Amumu is the only one with is ability.

His tantrum is very very effective against minions. If there's a whole horde of them, because of the passive, they can barely do anything to Amumu and reduce the cooldown by .5 every time they hit him. If there's 18 minions, you can use tantrum about once per second! And your despair can constantly damage the minions as well, for a good passive DPS.

Amumu is one of the best champs of dealing with Tower dives. Trust me, he is. I once got a double kill at lvl6 with him, when they turret dived. How do I do it? here are dome tips:

-Be careful, always expect a dive.
-Don't try to bait them into turret diving you.
-Don't be afraid to use your ult or q, those are your best tools.
-Never become an easy target

So now I hope you see why Amumu can be a great Crazy Eights player. His high DPS and tankiness make him an ideal jungler for every team. And you may ask why they always ban "the mummy"? Well, play him on normal and find out ;)

And kids, don't Cry this at home! ;D

This guide is being updated and revised. I only had a night to work on it so thoughts and comments will be appreciated. Good luck gankers. ;)