I only possess one Windows game - Civ III. I haven't been able to get it working on Linux either.
To run Windows programs in Linux, you need a program called Wine. It is included in the standard SuSE install.
However, for one reason or another, Wine isn't usually sufficient to run games. It certainly won't run Civ III as it stands.
There is an enhanced version of Wine, called Cedega (previously known as WineX), which is specifically aimed at gamers. A lot of games are reported to work with it, though I haven't heard anything specific about Civ III.
Cedega is a commercial product; to get the full version, you need to buy it from
www.Transgaming.com. You can download it for free (as with any open source program), but the commercial version includes some additional libraries that aren't open source, which deal with things like some copy protection schemes, so you won't get the full benefit from the downloadable version.
I can't tell you whether Cedega will run Civ III, as I never bothered to download it -- I wasn't really that desperate to play Civilization to install Cedega specially for it, so I just left it. (I'm not a big gamer anyway)
So I've said a lot, but not given an actual answer to the question... If anyone can give a definitive answer as to whether Cedega (or anything else) will play Civ III, I'd also be interested.