Well, that's a lie, I have had problems with old games, but that's only because I'm running the x64 version and old EXE's don't like that (unfortunately, not even compatibility mode fixes this problem).
So yeah, Win 7 definitely. It actually uses less RAM "out of the box"* than previous iterations of Windows (XP and Vista). Having said that though, more RAM is always better even if you don't need it. >4GB though and you'll need the 64 bit version.
*By out of the box, I mean a completely fresh install before you've started putting anything on it.
(Sorry, only just noticed I'm a few days late on this one <.<)
[Edited by Skyheart, 12/26/2010 1:12:06 PM]