Yesterday I was looking at the history of Pentax in the development of the fish-eye lens, and although there were other fish-eyes before the Takumar the key development was the enablement of using such a lens without having to use a tripod and lock up the mirror. There are also other types of fish-eye lens, with different geometric projections, and even some that exceed the usual 180 degree field of view, going up to 220 degrees. These are excellent for views that include our feet in the shot....
One of the key things with any ultra-wide, including the fish-eye, is to use it either to get a lot in, as in perhaps an interior shot, or to get in close and use dramatic foreground interest. If used like a standard lens then results are usually disappointing. It's a dramatic lens, so be dramatic and bold. Get in close, then closer.
There are two basic types of fish-eye - the full frame and the circular image. In this context, full frame means an image that fills the frame, be it with a FF camera or an APS-C one.
The circular image version gives us a 24mm diameter, circular image within the frame.
I have used various fish-eye prime lenses for the purpose of EPZ reviews, but my own lenses are the Pentax fish-eye zooms, the 17-28mm for full frame and the 10-17mm for APS-C. The latter is also available as a very similar (identical optically?) Tokina lens for Canon and Nikon DSLRs and the price seems very reasonable. There are also several low cost fish-eye prime lenses. It's also worth mentioning that Pentax make a tiny fish-eye lens for the diminutive Q system. The Pentax zooms are interesting as the fish-eye distortion gradually reduces as we zoom in, adding to their usefullness. It's also worth noting that fish-eye landscapes will look normal if the horizon is placed firmly in the centre.
So here's some examples of fish-eye shots.