It's not necessary, but I always do just to ensure that everything is working properly. A machine may appear to be working fine, but there could actually be a minor problem that will only show up after some extreme use. Stress testing will usually make any flaws appear so they can be solved before you're really in the middle of something, such as a game or a video encoding project.
I like to have peace of mind, so I stress test more than most people would. I do 24-30 hours straight with the following running simultaneously:
-Prime 95
-3DMark 2001 running the benchmark in looped mode
-Winamp 5 playing all my music
-Whatever hardware monitoring software came with the mobo
If that goes well, I repeat the 24-30 hour process with this:
-Prime 95
-Tribes 2 or UT2k4 hosting and observing a server with 6 or more bots
-Hardware monitoring software
That pretty much gaurantees stability. I did that to this computer (2500+, A7N8X Dlx 2.0, Corsair 2x256mb TWINX3200LLPT) when I built it 11.5 months ago, and it has never crashed.