A college degree is NOT the only way to do this.
The first thing you want to do is ask yourself what do you WANT to be doing when making games?
A CompSci degree isn't going to help you much if you want to make 3D models and animate them.
Then ask yourself, what skills for that role would best suit what you want to be doing?
Programming, sure, a general compsci degree will probably help, once you know how to think logically and program, you can jump to any language pretty easily. But then it breaks down to graphics engines (lot of 3D, matrix math and such), toolset, AI, etc.
Level and game design? Probably Math and behavioral sciences. Yes, really, behavioral sciences, think about it.
Character Art, life drawing, film and animation (gotta know how people move). Environment Art, landscapes, architecture, structural engineering.
By no means are these definite, but an example of how various roles rely on what might initially sound like unrelated ones. Obviously the more you know, the better you can apply all aspects when making a game (i.e. incorporate level design with architecture, and realizing it should be optimized for play on a mobile phone, etc).
Studios care less about degrees or which college or university you went to, and more about practical examples. Fill that portfolio with art samples or demos. If you have to, join a mod team and work on modding an existing game (Hey, UDK is free! [www.udk.com]).
Obviously having both helps. A degree shows you have the dedication to see something through to completion. Even better if the subject is relevant to the role you want to play (A PhD in Sociology might not work that well if you apply to be a concept artist). And the portfolio shows you have the skills to back it up, as they won't just hire you based on your word alone*.
Hope that helps you find your way, and good luck!
* Seriously, make me world dictator, I can do it, honest!
