There are cruises that specialize in younger crowds, and there are also groups that cater to "police, firefighters & men in uniform" which suggests a younger, more fit crowd.
If you and a friend go together on a short (3 or 4-day) Carnival, NCL or Royal Caribbean cruise, especially New Years or Spring Break, you will run into other single people most likely. I personally don't recommend sailing solo if your goal is to socialize, its better to have a friend along in case the cruise is a dud.
Shipboard romances are usually with people who live in other cities, and so continuing the relationship can be problematic (depending on who you are - some people can do it easily). But my point is, I think singles cruises should be about having some short term fun, a little flirting, whatever, but mostly about enjoying your vacation. I wouldn't personally go into them expecting to meet your soul mate, though anything is possible.
Once again, though, as Pat says, the shorter the cruise the younger the group will probably be.