Cthulhu Saves the World is a great 360 indie game, and is also available on Steam for PC.
LIMBO comes to mind. It's a puzzle-platformer with a monochromatic aesthetic and some really good puzzle design. I haven't played it on the 360, but since I was using a pad I assume the Xbox version is more or less the same.
I also really liked Bastion: it's got a really clever technique with the narration and a great art style.
I'm not 100% sure if this is what the OP means, but those two games are in the 360 Live Arcade Game section and not in the 360 Indie section.