My favorite binding that I have seen for modern books, particularly softcovers, is the "repkover" lay-flat binding.
The pages are sewn together in such a way that you can bend the spine >180 degrees and the pages will not fall out; in fact you are encouraged to do this so that eventually the spine will not tend to "collapse" the pages when open.

We first started using this binding for manuals published by a small non-profit I used to work for in 1992 or so. 11 years later I still rarely see this for anything other than a handful of computer manuals. Is anyone else here familiar with this binding? If so, why is it not more commonly used?