I first purchased a fish-eye lens in 2012. That was an ASP-C f3.5/12mm lens that found much use for my "Looking up" series. When I bought the full-frame f2.0/6.5mm lens, I was able to triple the scope of my viewing to 190°. In contrast to the older lens, the new one produces a round image.
Here is the same room (the baroque palace in Ludwigsburg) taken with the 12mm (effectively 18mm) and 6.5mm lenses:
Obviously, if you are photographing people, you have to be careful to not have them at the edge of the picture because they will be distorted. With a normal wide-angle lens the distortion will be the opposite, making them look broader.
The following pictures were taken in the gardens around the palace, also in Ludwigsburg. I've maintained the black border, left and right, as a frame.
As you can see, the fish-eye lens allows - almost forces - you to get up close to your subject, giving the viewer the feeling of being right there splashing in the water or smelling the flowers. The starburst appears when you close the aperture all the way to f22. I like that effect.
Which of these images is your favorite? Why?