Eversion is a really fun old-school style platformer. It's available for free and is very easy/fast to run. I highly suggest this game, it's a small file so check it out.
The game mechanics have a fun twist on 2D platforming. You can use the X key or Spacebar to "evert" the level. This power only works in certain areas and it changes the map, making previously unpassable locations passable. An example eversion is making all of the clouds solid so you can use them as platforms. Experiment to find the eversion locations. The maps are small, so it isn't difficult.
This game has a pretty big twist which I won't reveal and if you want to discuss the twist please use spoiler tags. Just try the game and you'll see why I had to blog about it. There is another freeware game I discovered tonight that I want to blog about but I'll save that till tomorrow.
So check out the game. Once you get into it, you'll see what I mean. I don't want to say much more, you need to play for yourself.