Well you can use someone else's network.
But think of things from this perspective: If you change your source IP, how will the server you are playing a game on know where to send all the game data packets to?
Example:
You are IP Address: is 192.168.1.16
You log on to Server @ 192.168.1.123
You run a "masking utility" that tells the server you are IP address 192.168.1.69
All of a sudden your game session freezes (and drops) because the server is sending all your positional and status data to 192.168.1.69... and you are still @ 192.168.1.16
You can "hide" your IP when browsing by using a proxy, but while there are http proxies all over I don't know of a single (efficient) "Game Proxy" server. It's theoretically possible, but you have to essentially MAKE one for every game you want to play, and run it at a remove site. It's not really feasible.
RAWR!