Cursor * 10 [1] (link via reddit [2]) at first seems a simple game—just click on the stairs to move up, with the goal being the 16^th floor. It's pretty trivial until the 8^th floor where you have to press a square to get the stairs leading up. But once you leave that square, the stairs disappear.
Quite the little puzzle until you realize what the rather cryptic message, “cooperate by oneself?!” (seen at the begining of the game) actually means—your past lives can help!
Each time you run out of time, you start over on the first floor, but so do all your previous lives. So the trick there is to get to the 8^th floor, and hit that square until you run out of time. Then using your second life, get to the 8^th floor, and wait until your “first” life shows up and hits the square, then proceed onward.
There are a few other places where you need past help as well.
It's not everyday you come across a multidimensional time-based game [3], although this game is a bit too frantic for my tastes.
[1] http://www.nekogames.jp/mt/2008/01/cursor10.html