At the popular level, Brian Greene's Elegant Universe is probably the best bet. Lisa Randall's Warped Passages is certainly good but isn't really about string theory.
I'd actually say not to bother with the books by Susskind, Smolin, and Woit that stargzr_htn
mentioned up thread. They're all of them playing out an academic war in the popular press, overselling their respective positions, and there are much better and more reliable ways to learn about the actual science.
At a textbook level, Barton Zwiebach has a string theory text designed for undergraduates, and the introductory chapter to the textbook by Green, Schwarz, and Witten does fairly well at conveying the basic ideas and successes of string theory in an intuitive matter.
In case it's useful, the classic texts are the one by Green, Schwarz, and Witten, and the somewhat more modern text by Polchinski. (Clifford Johnson also has a textbook, but that one I haven't read.)