I had the opportunity to teach an undergraduate course in algebraic geometry, and let me tell you that finding a book at that level was not easy. First, be aware that most books will not be self-contained and will farm out the necessary commutative algebra to outside references.

For a first taste, I would go with An Invitation to Algebraic Geometry by Karen Smith et al. (Springer) It's not really designed for undergrads, and I'm not sure how it would work as a textbook for a course; rather, it was written for people with a certain mathematical maturity who don't know anything about the subject and want to learn the basics. I recommend it because it's short, recent, good for self-study, contains a lot of the classical stuff, and it can give you an idea of the flavor of the subject.

There are tons of algebraic geometry books out there, so I'm sure other good recommendations are forthcoming.