ilves: If you're writing a story with a focus on characters, the apocolypse really isn't a vital portion to your story. It is vital that the people are trapped on the boat for whatever reason for a long-period of time. Granted, for a scale of years, it would have to be some giant disaster of some kind, but I'd say the better way to play it is making a side plot having the survivors try to figure out exactly what DID happen. Maybe they're out at sea and all communication stops, next port they get to is deserted (or something), etc. Just an idea though.
That's actually a much better idea. Keep the readers and characters guessing.
Also, it probably would be best for me to start out smaller. Write a short story focusing on a single character, and if it pans out, include him in the larger story.
And yes, it would be very difficult to keep it from going cliche. I don't want to re-tell Lord of the Flies, but I also don't want to make something that has a very clear-cut, happy ending. But it is a good idea to have a character who goes through redemption, like a dictator, prisoner or some other kind of criminal/prick.