You can generally a program like Prime95 to check for cpu stability.http://www.mersenne.org/freesoft/
Memtest86+ to check the memory(overnight at least)http://www.memtest.org/#downiso
While you can test your video card, chances are your gaming will test it more then enough for you.
In general a system with an unstable cpu or memory will be crashing anyway and memtest/prime are used to see what is failing. Prime95 can actually detect memory errors with its blend and custom tests as well.
When you run Prime95, your cpu will be loaded more then most of your games/applications so if it is stable under that, it should be stable.
Some users have a different time they want to run it for(some errors take very long to show up). overnight is good enough for most users.
Hope this helps and enjoy the new system.