To be honest I felt that Q was most effective when used sparingly. He was an all powerful being, a living deus ex machina if you will, and I think that it's very difficult to write a good story involving such a character. The few episodes he appeared in weren't always the best, as it was.
We should probably be thankful that they never attempted to make a Q movie. The banter between Q and Picard probably would have been exaggerated to annoying proportions. It would have been two hours of Q doing crazy things to Picard and mocking him, while watching Picard try to visibly restrain himself from face-palming. Like a sci-fi Odd Couple movie.