What are you formatting? An windoze system? A Mac?
If the games are windoze, they won't work under Linux, unless you can run them through Wine, or some other linux software that will run windoze code. There are a ton of Linux games to install and try, a lot are free.
Some things to consider before you wipe out your system. There are Linux distros like Kinoppix that will boot from a CD and do not need to be loaded on a hard drive in order to run. I would suggest you try one like that first to find out if you like linux enough to warrant the work.
Second, if you like linux, and want to install to a hard drive, consider a dual boot system. You don't have to give up your old system as you learn linux. There is a learning curve, it can be long and frustrating. Keeping the old system around lets you keep a running system while you learn linux install and configure linux.