I have C++ Primer Plus by Prata (5th ed) and it is an excellent book as it assumes no prior programming experience and will serve as a good reference later on. It's size may be intimidating but if you really want to be a good programmer with C++, it is well worth the effort. This book was much more helpful than my assigned texts during college.
Most of the books in the link provided by gerard4143, might be too advanced for someone who is just learning the language (i.e. Myers Effective C++) or do not provide enough depth of the language (most of the Sam's 10min/24hrs/etc. books). Even though Stroustrup designed the language, I found his book to be a bit cryptic when I was starting in C++.
After Prata's book, I would suggest considering something like Scott Meyers books. When you get to that point, you should be able to decide for yourself what you'll need.
I have to stand up for Ivor Horton's Beginning Visual C++ series. The 6.0 version of his book has served me well. The 2010 edition teaches C++/CLI as well as C++. I think he has a title that is pure C++, but you may want to look around for it because I don't know the title.