As an OU student I use them lots as somewhere I can work and not be distracted by the internet, (hi!). My favourite local one is Epsom, as whoever designed it was sensible enough to put the children's area at the opposite end to the area with desks for working. I also like Elephant and Castle library, as everyone in there is so hard working it makes me feel I can't procrastinate because I'll be looked down upon. My most hated library is the Shepherds Bush one right next to Westfield - glorified internet cafe. I appreciate the need to offer that service too, but at least leave a few desks without computers on them.
Lets talk about libraries.