The PlayStation 2 and 3 are capable of running Linux, although with the PS2 you won't be able to use the disk drive and uses your memory card and a hard disk, so you'll need an old PS2 model.
For the PS3, you can run Linux on that, which then you can install Windows XP on but from the video I saw on youtube, it was very slow. On the original Xbox, it is possible to run WIndows 98. The main problem is getting drivers to support the graphics hardware, so you can actually get above 16 colours, or with Windows XP, at least 3D support.
While some games to run on Linux, unless it's your ambition to play Solitaire on the Xbox, it might be more hassle than it's worth.