Pros:
It lets you run some programs that are restricted by the default permissions. Search the marketplace for "root" to see a list of them.
It lets you load custom ROMs.
Cons:
It voids your warranty (once you're rooted you can mess with the CPU clock and fry/prematurely age your hardware, among other things).
It's much easier to screw up your phone.
It exposes you to more security risks (once an app has root access it can do what it pleases).
Don't root just to root (unless you want to learn the Android guts, in that case don't use the one-click method but learn how to SBF). Figure out what it is you want to accomplish and then we can help figure out if you need to root or not.