I've had this problem with a few games under WinXP. The problem is that WinXP is a completely different system underneath the fancy interface. Win ME and below were based on DOS, which many older games used and, in many cases, relied on this fact to run. Some will run under XP, but many need a patch for the game to run properly.
Another side to the problem are the video and sound card drivers, as these work differently as well. This was the biggest problem I was having with old games under XP. Win 98/ME would allow programs direct access to the hardware, which many developers took full advantage of. XP doesn't in order to help make the OS more secure and stable. For me, using the newest ATI drivers fixed the problem, so you might want to have a look at that too.
As a last resort, and one that requires quite a bit of work if you only have one or two games, is to partition your hard drive as mentioned. If you don't have a large drive, this can also waste a fair bit of space.
Good luck and let us know how it goes
goates