First, you need Stroustrup's "The C++ Programming Language", at least the 2nd edition. It's useless as a tutorial, but it is the definitive reference. Keep it around for looking up those obscure answers to even more obscure questions later on.
To start, I'd recommend Bruce Eckel's "Thinking in C++". Eckel's "Thinking in C" and Thinking in JAVA" are highly regarded (I have the latter, and I like it). Although I don't have the C++ book, I have no reason to believe it's quality is less than the other two. As it turns out, I found the book rendered in HTML [link|http://www.iiitb.ac.in/Documents/c%20c++%20oop/thinking%20in%20c++/tic_c.html|here!]
HTH