What are good books to learn graph theory? What are some of the best books on graph theory, particularly directed towards an upper division undergraduate student who has taken most the standard undergraduate courses? I'm learning graph theory as part of a combinatorics course, and would like to look deeper into it on my own. Thank you.

I learned graph theory from the inexpensive duo of Introduction to Graph Theory by Richard J. Trudeau and  Pearls in Graph Theory: A Comprehensive Introduction by Nora Hartsfield and Gerhard Ringel. Both are excellent despite their age and cover all the basics. They aren't the most comprehensive of sources and they do have some age issues if you want an up to date presentation, but for the basics they can't be beat. 
There are lots of good recommendations here, but if cost isn't an issue, the most comprehensive text on the subject to date is Graph Theory And Its Applications by Jonathan Gross and Jay Yellen. This massive, beautifully written and illustrated tome covers just about everything you could possibly want to know about graph theory, including applications to computer science and combinatorics, as well as the best short introduction to topological graph theory you'll find anywhere. If you can afford it, I would heartily recommend it. Seriously.  
