Laurent Perron gave an interesting talk at CP'11. Laurent was in charge of ILOG CP Opt and he is now at Google developping the OR department. During his talk he made this remark: "ILOG CP was an expensive product, thus we had only complex problems that were very difficult to solve. When a product costs a lot of money then the companies are interested in it only when they have a very complex (and difficult) problems. Or-tools (the Google CP Solver) is mainly used in internal by Googlers and most of the time for solving easy problems. Almost all problems that we solve everyday are easy." I also remember that Laurent explained to me that he received requests for solving "simple" questions like : enumerate all the possible combinations of these variables. If you need to write such a code from scratch this is not an easy task at all. In fact, some people would like to have a simple tool for writing things like "for each combination of values in this array satisfying this constraint do something". In this case CP is really a good answer.
So maybe the answer about the problems solved by CP is the one proposed by Laurent and that is verified at Google: 99% of the real life problems arising everywhere :-)