What are some good programs to run after building a new PC? Any benchmark programs or anything else I should know about to make sure everything is running ok?
Use Orthos and Prime95 to burn-in your processor and memtest86+ to stress your RAM. As SC385 mentioned, use PCMark and 3DMark to benchmark your computer (3DMark could also serve as a stress test, though a poor one by itself, for your graphics card.)
But it's an incomplete list. You'd get better answers by searching the General Software forum first.
Processors don't need to be burnt in. They're not boots
If you're going to overclock, you will want to stress test your system to make sure that your overclock remains stable under very high loads. Orthos is useful with Dual Cores, but it's only a pretty shell for an older version of Prime95 which won't properly stress Quads w/o user intervention. If you have a Quad core, Prime95 25.5 is the most popular stress test for determining CPU stability. Be sure to run the Small FFT torture test and to enable rounding error checks before you begin.
Another useful program is OCCT, which many find to be a better stresser than Prime w/o raising temperatures as high. It's also more useful when trying to find a max overclock, as when you have an unstable configuration, OCCT tends to error sooner than Prime.
Yah... what Mark said. The only thing that would need "burn-in" is the thermal compound, depending on which one you use. However, performance of the thermal compound is supposed to improve over time, again, no real need to "burn-in" anything.