I wouldn't be surprised if you didn't even have a favorite XBLIG, whoever you are clicking on this thread. Though there are over 2500 games on the Indie Marketplace, only a handful of them are actually good.
My personal favorite XBLIG is a little game called Super Amazing Wagon Adventure. Like the title of the game says, it's just amazing. It's funny, fun and looks and sounds great (for what its trying to be). I have the only review on the site so far, and hopefully my review can persuade some of you to buy it and share in the Super Amazing Wagon Adventure.
There are some more good XBLIG I can recommend, though. The first being Wizorb, which is probably one of the better known games on the service and has been covered more than a few times on this GB and even has a Quick Look. Dead Pixels is a fun zombie game that plays kinda like River City Ransom mixed with a Grindhouse style. I MAED A GAM3 W1TH Z0MBIES!!!1 has to be the best known XBLIG out there, and with good reason. Its just fun and that song is amazing. Then there is Beat Hazard. A really unique game that plays like any other dual-joystick shooter, but the waves of enemies change depending on the music you're playing in the background (Quick Look)
So now that I've shared with you my favorite Xbox Live Indie games, what is/are yours?