HDR most assuredly has its place. In a low-light situation, for example, you can take multiple photographs at differing exposures and blend them into a composite that will look better than any single image. We used to have a couple of members here who created really great HDR composites.
The first thing to do, in my opinion, is to look at a photograph and ask yourself if it's an HDR image. If you can answer "Yes!" without any doubt then it's overprocessed. Likewise, if the colors are blazing there is zero question about it being overprocessed. If you have to think about whether it is or not then it was pretty well done.