That's a fisheye lens (or a simulation thereof -- I didn't look very closely).
You can get fisheye lenses for most SLRs. I'm not sure about one for your Finepix though. I believe there are some wide-angle converters around, but I'm not sure 1) if there's one to fit that particular camera, 2) how well they work in general, or 3) whether any even attempt to give nearly that wide a view anyway.
You can simulate a fisheye in software fairly easily, though the exact quality varies fairly widely. Just for example, Hugin will let you enter lens parameters to describe its distortion. This is intended to be used to remove the distortion, but if you enter the right values, you can just as easily use it to produce distortion.