You can run stress tests to check if it's stable, and benchmarks or similar to look at performance.
Examples of stress tests would be Memtest86+ for memory, Prime95 for the CPU, and Furmark for the graphics card.
Benchmarks could be things like 3dmark, Unigine Heaven, Passmark etc.
Another option would be running Folding@Home, which uses the CPU and/or graphics card to generate useful data for biochemical research; it awards points based on work done, and the number of points per day indicate performance. Tom's Hardware has a
Folding@Home team if you're interested.