Seeing a fin like this out at sea always requires a close look — is it a shark, or something else?
If the fin sculls from side-to-side and occasionally flops over, then it most likely belongs to one of these:
This is an Ocean Sunfish (Mola mola), one of the largest (= heaviest) of the bony fishes. Although most individuals are ~3-5 feet long and weigh 175-500 pounds, the largest recorded was nearly 9 feet long and tipped the scale at just over 5,000 pounds!
If you haven't seen one before, Ocean Sunfish might be hard to figure out at first. Their anatomy is unusual. The caudal (tail) fin has been reduced to a ruffled flap along the trailing edge, so the fish looks dramatically truncated.
The most noticeable fins are the dorsal and anal fins — they're the tallest fins and are used for swimming. If you're looking for them, the pectoral fins are also visible at times — they're short and rounded, located behind the eye. Here's a picture that shows all of the fins I just mentioned (the sunfish is lying on its side at the surface):
The image above also shows the overall rounded and laterally compressed shape of Ocean Sunfish. This shape is alluded to in their scientific name — "Mola" means "millstone."
The mouth of an Ocean Sunfish is relatively small (this is a head-on view):
Below are two pictures in a feeding sequence. The first shows a sunfish approaching a Velella from below. In the second, the sunfish has just finished inhaling the Velella. (Note that it appeared to be using its rounded pectoral fins to steer.)
I'll leave you with one last shot of this wonderful open ocean fish. Watch for them this year as there seem to be quite a few around, perhaps associated with the warmer ocean water.
All photos from Monterey Bay on 22 August 2014.