I think this question needs clarification.
1) Fastest NETWORKED computing system
OR
2) Fastest single computer BOX
If it is 1, then it may be likely that the above answers are all wrong. There are several networks running medical and cryptographic problems and they are distributed world-wide. However, their computing power (flops) varies over time.
You can get more info by looking up "cracking DES" or stuff like that.
If it is number 2, then likely the answer will be something like "Cray" this or that or something.
Creating a "super-computer cluster" is relatively easy (Google for "beowulf" etc.). The system in the US with the Apple G5's was created in no time. They had originally planned a different system, but when number came in telling them that they could do it for a fraction of the price with Apple computers, they pulled up their sleeves and went to town. The rest is history.