Even though most games wont run natively on Ubuntu there is still a sizeable number that  runs flawlessly on it thanks to the almighty Wine.  The Wine app database lists a few games that run flawlessly on Ubuntu or any other Linux distribution for that matter and assigns  a rating for them based on precious metals.

Final Fantasy XI

GuildWars All Versions

StarCraft II Retail

Team Fortress 2

Left 4 Dead Full 

Warcraft III

Half-Life 2: Retail

Day of Defeat Source

Lord of the Rings Online Volume III

Counter Strike

Caution - Try installing these games at your own risk :-). We did not test out each individual game although we would  like to as it is practically impossible on our ancient rigs and most of the games listed here can have them for breakfast.. We based this post on the appdb ratings provided by winehq.com which had been tested by the wine community . 

Check out  Wine App Database ratings.