...it depends.
Welcome aboard, by the way. Check out the Water Cooler above, introduce yourself, look around.
Some games have native Linux versions: Quake 3, Unreal Tournament (I think), NeverWinter Nights, and a few others.
Many Windows games don't have Linux equivalents (Half-Life only has a Linux server, no Linux client) but strides have been made in the right direction using TransGaming's WineX (now Cedga(?) IIRC) plugin to emulate Windows services on the x86 platform.