Navies are pretty useful for bombarding cities that have bunkers and/or anti-aircraft stuff like SAM infantry. I've also done mass invasions with 4 transports full of my best troops to establish a firm beach-head, when I have no land route. Otherwise I just build a couple of ships per fishing boat tile and that's about it.
HOWEVER: I remember one game where my lack of a strong navy almost screwed me. I had only offshore oil and THOUGHT that a pair of battleships and a destroyer with Medic was enough to defend it, but I was proven wrong when 2 civs DoW on me one after the other, and the rest of my forces were far away fighting 2 other wars. A whole crapload of enemy naval units showed up. I knew I had 1 turn, 2 at the most before my platform bit the dust. So I switched to UniSuff and 0% science (thank goodness for Spiritual), bought some battleships and a workboat, and when they blew up my offshore platform, I quickly raced over and rebuilt it and guarded it with my newly-purchased battleships until my bombers from the other war returned in sufficient numbers to slow down the naval assault. I had to rebuild my platform twice during that game, but I always had a spare workboat in a nearby city to rebuild it on the same turn. Nevertheless it taught me the importance of having a strong navy when your only oil is NOT land-based.
Also, whoever said they just allow their fishing tiles to be pillaged and rebuild them with workboats after the war.. you're nuts. You lose commerce, a lot of food, and everything that entails, whether it's losing specialists (less food) or even starvation of the city if it was getting a lot of food from the sea. It's SO worthwhile to build some ships to guard your food. They get +10% on defense, which combined with drydocks, some civics, and/or Pentagon will allow them to fight defensively with the equivalent of Combat III or higher. Attacking offensively to deal collateral damage against a big ship stack wouldn't hurt, though. Add a medic ship for fun.