I like most of the suggestions so far.
We tend to keep it simple. We don't have the electronic games at home so that's not an option. Lots of books and board games. When the kids were too young to read on their own, my wife always had a chapter-book that she could read to them enroute in the cockpit. Books like
Voyage of the Dawn Treader, and any of the
Swallows and Amazon series (especially
Peter Duck!) make great reading aboard a sailboat.
Captains Courageous is a good one too.
Another old standby are books on tape/cd when parents are too occupied with sailing. If the kids' attention spans aren't developed enough for chapter-books, try short story collections from storytellers like Jay O'Callahan and Jim Weiss. These are usually available at local libraries. Also, if you can find a well narrated version of
Treasure Island, a good actor can read those pirate voices more convincingly than most parents.
When our kids were really young, we had a rectangular Rubbermaid storage bin, about 2'Wx2.5Lx1'D that we'd fill with water and set in the cockpit footwell to let them splash around in. Now they like to drag their feet over the rail or even hang in the bosun's chair.
At anchor, our kids have a blast with the sailing dinghies and kayak. We consider these "must haves".