Spring break is really a moving target. I am a school teacher and our spring break this year is 4-2 through 4-10. In Oregon, their spring break is two weeks prior. In general, I would say that any time from President's Day weekend through mid-April you are quite likely to see more kids than normal aboard ships.
You may wish to choose a line like Princess that limits the numbers of kids aboard each ship or choose a line like H.A.L. where the crowd is a bit more mature in many ways. I would definately avoid Carnival, NCL, and RCI if you don't wish to see quite a few kids.
The good news is that most if not all of the cruise lines do a very good job of keeping kids busy with fun and interesting activities. We always cruise during peak vacation times and have never been overly annoyed by children. (Knock on wood!)