I'm 25 and my fiance is 27 and we've taken two cruises this year, both on Carnival. We never had a problem finding people our age on the ship. Especially on the shorter, 3- and 4-day cruises, Carnival can have a very lively, young crowd! The nightlife on these ships is great.
Donna's right, lots of families love to take their kids on cruises, but most of the time the kids are shuffled away to the children's programs and you don't see them.
Our first cruise was on May 9, 2002 and that seemed to be a good time to go to avoid kids... too late for spring break but too early for summer.
Good luck finding the right cruise for you... it's out there somewhere!
Fantasy Fest in Key West