To put things in perspective, let's start with the computer sitting on your desk -- the computer you use on a day-to-day basis to browse the Internet, handle spreadsheets, create documents, etc. Most people have something like a Pentium computer running Windows, or a Macintosh. A computer like this can execute approximately 100 million instructions per second. Your particular machine might be twice that fast or half that fast, but that's the ballpark.
The fastest computer in the world is much faster than that, and it is sitting right on top of your shoulders! The human brain is an amazing computing device and the fastest processor available right now. Let me give you an example:
Your desktop computer is just starting to get to the point where it can "understand" speech and take dictation, translating spoken words into written words. It can only understand one speaker, and that speaker has to train it for about 20 minutes, and the dictation software will still make a lot of mistakes. So 100 million instructions per second can barely handle dictation.
Your brain, on the other hand, can understand any number of speakers. It needs no training and will make zero mistakes. It may even be able to understand multiple languages! And the speech processing portion of your brain is just one small part of the whole package -- your brain can also process complex visual images, control your entire body, understand conceptual problems and create new ideas. Your brain is made up of about one trillion cells with 100 trillion connections between those cells. We might take a rough estimate and say it is handling 10 quadrillion instructions per second, but it really is hard to say.
If you ignore the human brain and stick with electronic computers, then the world's fastest computer is IBM's RS/6000 SP supercomputer, which can perform more than 12 trillion calculations per second. The ASCI White, as it is known, performs at the speed of 12.3 teraflops (trillions of operations/second). That's thousands of times faster than an average desktop computer. But it's still not as fast as your brain.
Here are some interesting links: