I'm not familiar with 8 (and hope never to be), but from what I hear Civ IV works fine on 8. With that said, IV can have installation issues if not done correctly. Also, it may depend on where you purchased IV and in what format.
Try following the direction in this stickied thread from the Tech forum:
http://forums.civfanatics.com/showthread.php?t=408537
Much of the issues with recent versions of Windows has to due with user security, but there are workarounds for that that are quite simple. You should not have compatibility issues at all.