It depends. Some PC makers lock down their XP discs so they won't work on another brand. Dell does this. You may also run into activation issues, as XP will have previously been activated for that PC. Some people have success calling Microsoft and telling them they no longer own that computer, that its drive is wiped and the OS off for good, etc. This section's Reference sub-forum has a couple good threads on activation.
I also edited your thread title to make it more descriptive.