So I'm working hard at making Amumu a ban on sight champ.
Runes I have are Movespeed Quints, AD red, Armour yellow, CDR blue (AD red aren't really useful but I only have 2 rune pages), masteries are 9 Offensive for AP->Mag Pen and 21 defence.
Jungle Amumu, start with Regrowth Pendant and 1 health pot, start on blue with pull, then go wolves->wraiths->golems->-red->wraiths with skills being E, W, E, Q. Then time for your first gank, if there is no viable gank then jungle hard or just harass a lane, a good gank doesn't always have to end in an enemy kill, just forcing them back to base or using a flash is a success. Anyway after gank (successful or not) you should have enough gold to get Philospher's Stone and at least 1 boot, then go jungle some more, I like to focus E for the additional health, the lower CD's on Q are nice but at this stage you won't really have an opportunity to be using it twice in a gank so it's not urgent to level up so quick. Get Boots of Mob for incredible ganking power
Don't ignore the W though, it's nice and has a nice synergy with the next item you should be building, the mighty Sunfire Cape! Then work your way to an Aegis of the Legion (you can swap the order for Sunfire Cape and Aegis depending on how much gold you have as Aegis has cheaper ingredients) After that is done get an Abyssal Sceptre for incredible magic resist reducing powers when combined with your passive "Oh you have 70 MR, guess again you have 15 MR!" So far you are now pretty much a walking tank dealing shit loads of damage per second, clearing jungle and creep waves is just a few tears and a tantrum, now what next?
I like to get Will of the Ancients! Now not only are you a damage dealing tank you are a damage healing tank! For the final item you should sell of your Phil Stone for a Rabadon's Deathcap, if you don't have enough gold to buy it outright then just buy an Elesia's Miracle first until you have the gold as the extra regen and tenacity will outweigh the extra AP from a Needlessly Large Rod.
Also once you have full build don't forget to buy all elixirs, even the green one though that one for last. With this build you can basically turn any teamfight to your advantage, just get in there with a Q, stun everyone with an R, do a tantrum and chase any fools who try to escape.
There is only one negative thing with this build, it will give your teammates incredible over-confidence as you can stomp a baron'ed enemy team with your aura but if your not there then your team can fold like a 2, 7 offsuit.
I have only lost twice in the last 5 games with this build purely because my team kept on getting into teamfights without me from overconfidence and even as the jungler I ended up with 3k more gold then next highest person.
Now I know a fixed build can be silly but for Amumu I feel this build is pretty perfect, you have enough health, armour, mag res and damage to be a true all round great, all the items synergise well with each other and are great for teamfights. Even though you are a pretty tough tank you can still end up with 434 AP (with no AP runes) to deal huge damage of which most is AoE.