For the last year my only gaming computer has been a netbook (Asus EEE 1015PEM, dual core). It has worked very well for quite a few games. Naturally you don't want to push it too much. Before investing in a game, you'll want to search to see if your particular netbook runs it.
Since you don't have an optical drive or the horsepower for newer games, GOG is your friend. I have rebought a lot of games that I already own, just because it's much easier to install them the GOG way.
Your mileage will vary depending on your exact hardware, but on this netbook I've had great results with:
Civilization III (I heard that IV is very slow so I haven't tried it yet)
Baldur's Gate (I'm sure the other Infinity Engine games will work just as well)
Might & Magic 6, 7, 8
System Shock 2
Others, like Neverwinter Nights and Gothic 2, run but can get a little choppy.
Thanks to the netbook's portability and convenience, I've done more PC gaming in the last year than I'd done in the previous 2-3. Finally I'm catching up on my backlog of old games