HDR is only really useful if the dynamic range of the image can't be captured in a single exposure.
So, the typical successful HDR images are landscapes (with a large tonal difference between the sky and ground), interior images (churches are good candidates, where you get a range between the bright stained-glass and the darker interior areas), night-time cityscapes (lots of range between the bright lights from buildings/cars and the darker areas).
True (multi-image) HDR portraits are pretty much impossible since people would move between shots, though you could alway composite an HDR background with the person. Not to mention that the increased contrast of HDR is very unflattering to the skin tones.
If you like the re-contrasted look of HDR images, but you have just a single image that already has the full range, you can still use HDR processing on it, but you can pretty much get an identical result using the Shadows and Highlights tool in Photoshop, or anything other processing that increases
local contrast (link to a PS action I made that does the same thing with layers).