It's a little silly to say, but the obvious answer would be "for problems where the GPU is better than the processor." A modern graphics processor has more than a thousand cores, but a relatively small amount of memory, so in general this means that it is well suited for parallelization and does not do this, t take too much memory.
G. Bach mentioned rude attacks on cryptographic material in the comments, which is a good example. Scientific simulations are another good example, in fact, several research institutes (in particular, NASA) created clusters for modeling the Playstation 3. Several Wikipedia articles on GPGPUs list several applications of this technology.