Is it possible to land a 737 on an aircraft carrier?
An unloaded 737, flown by a top-tier pilot can stop incredibly fast, generally in a shorter distance than a Cessna-172 flown by a student (typically around 900 ft:  I've seen planes at Boeing Field, land 32L and stop well before A9).

Because the brakes are meant to stop a fully loaded plane on a wet runway, they are extremely powerful when the plane is empty and the braking action is good.

Although it has never been attempted (to the best of my knowledge), I think a 737, near empty weight, in optimal conditions, could likely land on a carrier with a 1,000 ft deck steaming into the wind (lets estimate headwind + carrier speed for a combined effective wind of 50kts).

Another consideration, however, would be if there's enough space for the 737's massive wing span.