This is one of those cases where I read something and I say the author is brilliant but really I dig it so much because he agrees with me. These truly are good candidates for the five most important books for a programmer to read.
It has been a long time since I read Code Complete. As I recall it had lots of C code in it. It was still a great read. Of all of the books I'm not sure this one should be here. Maybe I'm getting it confused with Writing Solid Code, another Microsoft book on writing software.
If you liked the Pragmatic Programmer book you should read My Job Went to India. It's a great continuation to the book with outsourcing as some additional motivation.
The Larman book, Applying UML and Patterns is another good one too. If I had to pick one book, this might be the one. It shows how to apply UML to design and it makes sense of process.
Design Patterns is essential but can be dangerous. Many programmers have showed up to work Monday morning with a skip in their step aching for a chance to apply the most recent design pattern they learned no matter how contrived the situation is.
Refactoring by Fowler is great because it gives you an opportunity to peek over the shoulder of Martin Fowler to see how he slings code at a very low level. How often he runs tests and how he moves code around. The Computer Science program I went through didn't give us any idea how to develop software at a low level. I wish I had this book when I first started.
Beyond that list, if you're doing Java, Effective Java by Joshua Bloch should never be too far. It's a great reference to keep around even after you've read it. It was a good book to read in the sense that if you're going to be writing an API you'd better get your sh*t together.
I'd replace Code Complete with Patterns of Enterprise Application Architecture, also by Martin Fowler. It's a great language-agnostic book that has had lots of influence. The Rails guys directly lifted Fowlers Active Record pattern.
In the comments to that blog posting a lot of people mention the Mythical Man Month. I'm ashamed to admit that I've never read it. I've read summaries and the main points and I kinda think I get the gist. A lot of the book seems intuitive.
In a top 5 list now days I'd like to see a book devoted to an agile methodology. The Schweiber book on Scrum would be good. Maybe XP Explained.