I think I can confidently say if you are only going to own 1-3 books on programming, that none of those books should be specific to any programming language, and by that criteria, I would have to recommend:
1. The Art of Computer Programming (It's a multi-volume set but I'm calling it one book) 2. Structure and Interpretation of Computer Programs
3. Code Complete
I can't argue with you there. That's good advice. I am not that sold on Code Complete though. I have read it and keep a copy on my shelf but I don't think it's one of the best. I would go for:
1) The Art of Computer Programming
2) Introduction to Algorithms (CLRS)
3) Elements of Programming