Platform games are a game genre characterized by jumping to and from suspended platforms, and indeed to be able to fall from or miss platforms as well.
These are really the only defining characteristics as there are exceptions to to any other suggested criteria. It has been suggested that platformers must have a jump button, and indeed nearly all of them do. Many more platform games to come.
Very basic platform game no doubt inspired by the Mario Bros games. Just use the arrow keys to control Dave and space to jump. Get Dave to his tree house at the top of the level to move on. Just jump through the gaps to reach the top.
Original Sonic the Hedgehog
What can I say. Run around collecting the rings and avoid the other animals and drops. Play as Sonic or Tails.