Originally posted here by slarty
If you want a definitive work, get

"The C++ Programming Language" by Bjarne Stroustrup

On the other hand, it isn't for beginners, it isn't easy to read and it doesn't really explain a lot of things very well. It has many chapters about STL and algorithms, stuff that C++ programmers really should be using.
I like the combination of "The C++ programming Language" by Stroustrup and "C++ How to Program" by Deitel & Deitel. Those are probably my two favorite C++ books.