My most common use is to chat on VeriChat while browsing the web at the same time, much the same as I do when I am at home using my PC. At times I will even play a game of Brickbreaker while the other 2 programs (broswer & verichat) are open.
The only device I have used that was able to multitask as good was the Sidekick II, but while the device is wonderful, the danger proxy server is too unrealiable and the web browser would time out too often. So far since having the blackberry, the web browser has never timed out on me. It always loads the page even if it takes a while to do so.