EDIT: I found this book to be a pretty great primer on the subject: http://www.amazon.com/Space-Elevator-Earth-Space-Transportat...
Here's a great book that came out of a NASA funded study that breaks the issues down well, including costs, necessary tech, and methods for dealing with potential issues like cable breakage: http://www.amazon.com/Space-Elevator-Earth-Space-Transportat...
Their conclusion was that it would be much more cost effective than most people think, and that it would enable an incredible reduction in cost to orbit due to not needing to use a pyramid of fuel to carry other fuel for later, or enormous one-time-use precision machinery, and instead using simple containers with electric motors and transmitted electricity.