Braid is the perfect example of the type of game that couldn't exist without XBLA and Summer of Arcade. It's a smart, bold game with interesting storytelling, mechanics, art, build around one of gaming's quintessential genres, the 2D platformer.
You'll probably notice parallels to a particular classic franchise: The goal of Braid is to... well, it's to save the princess. Hero Tim is looking for his princess, a woman who we lost a long time ago. At the of beginning the game, the story is told in broad strokes, but as players solve puzzles to collect puzzle pieces, Tim's memory becomes more detailed, revealing that the situation is more complex than a simple rescue mission.
Braid's use of recognizable tropes that gamers will recognize, both mechanical and aesthetic, is no accident. Aside from platforming, hero Tim has the ability to go back and forward in time. The mechanic, which literally allows you to undo most movements going all the way back to when you first began a given puzzle, allows players to adjust the position of elements aligning things perfectly for Tim to reach puzzle pieces.
The deep connection of the game's design and story make it a unique experience not to be missed.