Do You Think Artificial Intelligence Is Possible?

I'm about to graduate with a degree in computer science, and I don't believe it will ever be possible. When you break it down, most programs are simply if/else statements; logic written by the programmer. In order to become "self-aware" like in "The Terminator", wouldn't it have to continuously and knowingly re-write itself? I guess if it was being run by some sort of biological CPU, it could evolve, but I don't see that happening. Anyway, what do you think?