Fighters can be very useful against ground units. They're cheap, very fast, and they got quite a decent attack value (4).
I use fighters when I'm struggling to keep a city on some enemy continent (you know, imperial overstretch). Your fighter may go deep into enemy territory, looking for easy targets like unprotected artillery.
Another good thing about a fighter is that - like bombers and nuclears - it has a visibility range of 2 map squares, so it's a good scout. Nuclears make even better scouts because of their even larger range.