I recommend the trivia game(s). My wife and I have won them on almost every ship we've sailed on. Carnival gives you a "ship on a stick", a little tacky trophy. Holland America gives you ceramic mugs. Princess gave us a luggage strap.
I wish their trivia would have some "real" prizes like the bingo does.
Make sure you attend the "not so newlywed" game - it's a hoot!
And ask your waiter about the galley tour - it's always fun to do.