For really old games there is DosBox, others will work using windows XP's Win95 compatibility mode, this usually involves right clicking the games.exe and selecting win95 compatibility before install.
I think Half Life works with XP anyway.
If you're using Vista, likelyhood is that old PC games won't work with it at all.
Mainly though there are workarounds or solutions for most older games with XP, although there isn't any standard fix, the method changes from title to title, some have work arounds, some have patches, and some require third party emu's like DosBox. Your best bet is to google per game something like, '[gamename] XP compatibility' to find out what the best fix is.