I appreciate HDR technique for two reasons: First, it gives us an ability to take a picture and give it a very interesting "illustrated" quality. Second, and on the opposite end of the scale, it has the ability to create "superexposed" images that really allow you to bring the details in highlight and shadow regions more into line with what the human eye can see.
How an HDR turns out really depends upon the processing techniques used. I've had some neat HDR images turn out both ways, and I can say the ones that turn out well with one technique often look like hell with the other. Realizing that, I've learned what to look for when looking at a scene and trying to determine it's "HDR worthiness." I've also learned that, more often than not, I'm completely wrong about what I thought would make a good HDR. I sometimes benefit from "happy mistakes."
My personal preference, although I've turned out a fair degree of decent HDR in both types I described above, are the types of images that are HDR, but aren't very obvious.