How to run Counter Strike 1.6/Source in Ubuntu

Yes, it is possible to do this over Counter Strike. This site has all the info you need: HLSS.

Here's a couple of guides:

Counter-Strike 1.6
Counter-Strike: Source

The best option might be Condition Zero instead of plain CS 1.6

Z-Bot works still fine with the Steam Version:

• Download and extract the ZBot ZIP-File
• Copy all files (except liblist.gam and commandmenu.txt) to your ...\Steam\SteamApps\\..\cstrike directory
• In the Steam Game Library -> right click on Counter-Strike -> Properties -> Launch Options and add -dll "dlls\zbotcz"
• Now you can run the game