Originally from Ken Jennings:

Well, yes, sea captains can marry someone. In fact, in eleven states and many foreign ports, a sea captain can now marry another seafarer of the same sex. But what they’re not allowed to do is marry other people—that is, officiate at wedding ceremonies, pronounce that couples arrrr! now man and wife.

The popular romance with the idea of a wedding-planning skipper is so deeply engrained that both the United States and British navies have had to issue rules explicitly reminding their officers that they’re not allowed to perform weddings at sea. (Sort of makes you wonder how many mixups over unlicensed marriages led to these new rules.) The same goes for civilian captains.  Every U.S. state has its own list of people whose job titles allow them to solemnize marriages (typically judges, ministers, mayors, and the like) but so far, no state has specifically added “salty sea-dogs” to the roster.

Of course, if a skipper really needed to officiate at a lot of weddings (like, say, Captain Stubing on ABC’s The Love Boat) there are workarounds. In some states, like California and Massachusetts, the skipper could come ashore and file for a 24-hour marriage-performing power-up at his or her local courthouse. Alternately, an outfit called the Universal Life Church claims that every state but Pennsylvania and Virginia will legally recognize marriages performed by one of its 18 million clergy members—most of them regular folks who paid $5 online in order to order to be “ordained.” I’m sure that some of them, somewhere, are even sea captains. You may now kiss the bride, matey.