http://en.wikipedia.org/wiki/Goblin_shark
The theory: Leo Fender saw a Goblin shark sometime around 1949, it made a huge impact on him, and instruments changed from the influence.
Here's what the earliest Fender guitars looked like, before Leo Fender first saw the Goblin Shark (notice the headstock):

The headstocks were then changed to resemble the tail, and then finally the body horns were added in tribute to the fins. Finally he ended up with this:

...of course, I could be wrong!
