The answer is the half-price booth at Leicester Square. They sell tickets to the shows the same day at half price (or near half-price). Turn up in good time (I think they open at like 10 or something) and decide from posters outside what show you want to see. Don't expect to find the biggest shows here though. We went to watch "Damn Yankees" with Jerry Lewis. I had never heard of it nor have I read anything about it afterwards but it was really good. My feeling is that most musicals probably are!
Enjoy!

