I am slightly opposed to the "most likes" idea, as they tend to just turn into a popularity contest. I have seen many horrible posts win the prize (based on relevance to the contest subject) due to member popularity.
a pic of an actor/musician as a child and make people try to guess who it is
Battleship type game where you pick a square on the grid and the contest runs until all squares are taken, then pick a winner (or a cut off date in case there is not as much traffic as you would have imagined)
"Biggest cloud of vapor" photo contest - users taking pics of the biggest vapor cloud they can muster (maybe with a rule like "please include a penny in the pic for size reference")
A Where's Volt game where you hide a volt (or pcc) in an image and people have to find it