After I get my system built and OS installed. What are good tests to run to see if the system is stable?

Prime95, Memtest86 are two of the biggest stability / part tests.  SuperPI is another common test used, also a performance indicator.

 
Agreed these are both good for testing system stability. For your graphics card, you can do a graphics card stability test through the Nvidia contol panel or I believe through the ATI control panel as well, depending on what card you have.
 
Also it may be worth getting CPU-Z just to check all the components are running at the correct frequencies as listed by the manufacturers eg checking the timings of your RAM and the speed of your CPU.

Thanks for the help. I am running Vista 64-bit. Video cards are 8800GTS in SLI config.
 
Are Prime95, Memtest86, SuperPI and CPU-Z all free and just have to download them from the web somewhere? Will they also run on Vista ok?

They are all free.  Memtest86 is a utility that runs at boot (so you'll need to make a boot disk or burn it on a CD).  I don't know about Vista capability for the others, but I believe they are fine.

not sure about the others but cpu-z and prime 95 definetely work with vista 64