Many games which are available for Windows can be run on Linux by using an emulator, such as Wine or Cedega.
These emulators only work on x86 (Intel-based) computers, and will not function on AMD64 or PowerPC computers.
Wine (free)
Wine is free software, and is able to run several popular games, such as World of Warcraft and Unreal Tournament. For information about Wine, see the Xubuntu wiki.
Cedega (commercial)
Cedega is based on Wine, but is optimized for running Windows games. Cedega is commercial software and is therefore not free, but it is able to run more games than Wine. For information about Cedega, see the Xubuntu wiki.