Alright, I exaggerate somewhat, but "String theory for bright undergraduates and other mere mortals" doesn't quite have the same headline appeal. While browsing through Foyle's bookstore yesterday, I happened upon a most fascinating book, namely Barton Zwiebach's "A First Course in String Theory": what makes this book particularly interesting is that it purports to give a serious introduction to string theory without requiring the prior knowledge of quantum field theory and general relativity which is normally expected of those looking for something more substantive than a Brian Greene-style popularization. Written by a string theory partisan (who else would bother to write such a textbook?), it's probably not the best source to consult for a highly critical examination of the assumptions underlying the whole string theory approach, but if you're not intimidated by a little mathematics and are looking for a starting point to understand what it's really all about (reading "The Elegant Universe" does not qualify), Zwiebach's book seems to be the way to go.
PS: For interesting comments on the book and undergraduate courses which seem to have been built around it, see the responses to this post by Peter Woit.