Braid is a puzzle platformer where your main method of solving puzzles is time manipulation. By pressing the Shift button, you can rewind time back as far as you want and erase any mistakes you've made. This mechanic isn't used as an excuse for ever-so-impossible jumps, though; it's used to provide some of the most ingenious puzzles you've ever seen.
Every world after the first has a new way to manipulate time, starting with some objects that are immune to any time effects. My personal favorite is World 4, in which walking right moves time forward and walking left moves time backward. The last puzzle in that world, Fickle Companion, is particularly brilliant- it features a key that isn't immune to time effects, meaning that you can hold the key when you walk right, but the key follows that exact path backwards when you walk left. Good luck getting the key to where it needs to go.
By the way, if you're thinking of getting Braid, don't read any spoilers or hints. Actually, scratch that- read this
walkthrough before you get the game.
The demo and full game can be found
here.
