Just to prove that AP Rammus is not crazy, I did some quick calculations (although you could just try it out in the game and check the damage graphs afterwards).
The base ability power from items in this build is 170 not including the Elixir of Brilliance... that's respectable but not huge. Due to bonuses from the masteries tree, that gets an additional 0.6 per level and an overall 4% increase. Total ability power is thus 188, although for some reason Mobafire does not include masteries in the total displayed.
Now in an ideal situation, you powerball into someone (probably 2 champs take the hit), then activate tremors and DBC while surrounded by the entire enemy team. Assuming you didn't have to retreat, you may chase them down with a powerball to finish them off, but let's disregard that final powerball damage since we are being generous by assuming you rammed two people initially when beginning the teamfight.
So the bonus magic damage from the your two Abilty Power items breaks down like this:
How much bonus damage from AP?
Rammus base Ability Power = 0
Ability Power from items = 170
After applying masteries = 188
Targets = 2
Rate = 1.0 * AP
Bonus Damage = 376
Targets = 5
Rate = 0.3 * AP per second
Duration = 8 seconds
Bonus Damage = 2256
So the total bonus magic damage from buying 170 AP is up to 2632 damage per teamfight. The magic penetration aura will also help your casters to hit harder as well. Remember this is bonus damage on top of any damage that the skills would already do.
Targets = 1
Rate = 0.3 * AP per second
Duration = 8 seconds
Bonus Damage = 451
Remember this is bonus damage on top of any damage that the skill would already do.
To put it in other terms, the modest amount of AP in this build will be enough to increase Rammus's Powerball TOTAL damage by 63% and his Tremors TOTAL damage by 29%. Not a shocking amount maybe, but still quite useful.
The core items of the build which increase your Area of Effect damage are these two:
Abyssal Scepter, and
Whichever items you change or remove, do not remove those two. Also, there are very few situations where you do not want a Thornmail, so that is the third most important item.
Thornmail, ton of armor and brutal passive
If you are just crazy about maximizing damage or the enemy team is hopeless then Sorcerer's Shoes I suppose are a viable choice. Mercury's Treads however, are not needed, as you already have Cleanse and the
However, since this build relies on moving during the team fight to obtain the best position for maximum continual AoE damage, the only realistic choice of boots should be these babies:
Boots of Swiftness
Next we come to the less essential items.
While expensive and not essential, the hourglass has such great synergy with this build it would make little sense not to take it. It gives a ton of ability power which helps your Tremors and Powerball damage. It also has armor which complements your Spiked Shell and Defensive Ball Curl damage. Finally it has an active that will be very useful in the late game when there is so much damage going around that the enemy team could nuke you within an inch of your life faster than an eyeblink.
Two seconds of invulnerability may not seem like much, but in a late game team fight it can make all the difference in the world. The icing on the cake is that your Tremors damage will keep hitting the enemy team while you are invulnerable.
Finally the most expendable item:
Now you may be asking yourself, why would we want to slow the enemy's attack rate? Isn't Rammus doing more retaliation damage the faster the enemy attacks him? True, he is doing more retaliation damage, but he is not invincible you know. Eventually he will die and we don't want everything to happen so swifty that we don't have time to react or escape before his lifebar is completely wiped out. Remember there are other teammates doing damage and it is not all up to Rammus to finish the job!
Another thing about Randuin's Omen is that it has some nice HP regen via Warden's Mail, something the build would otherwise lack, and that keeps his lifebar completely full even as he is jungling or powerballing into wave after wave of enemy minions.
Something else I find is that Rammus doesn't farm very well in the early game because his attack is slow and he can be harassed by ranged spells. The Heart of Gold addresses his early game problems, and I hate to sell it later; that would kind of defeat the purpose of earning the extra gold in the first place. Since Randuin's Omen builds from Heart of Gold that is another consideration in its favor. Finally, the active ability can be used offensively or defensively which adds to Rammus's tactical options.