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According to the Xbox LIVE Arcade page on Wikipedia, as of November 30, 2011, 449 Xbox LIVE Arcade titles have been released for the Xbox 360. Produced by both major publishers and independent game developers, these titles tend to be smaller downloadable games than their retail counterparts. As such, they are often cheaper, generally costing between 800 and 1,200 points, or $10 and $15, respectively. Another feature that these games share is that they have leaderboards, encouraging competition among players.
The best place to peruse Arcade Games on your Xbox 360 is under Game Type on the Games blade under the Game Marketplace, where it is the first option. Other options include Games on Demand, Indie Games, and Xbox Originals. After you select one of these categories, you can further refine your search by using the Release Date, Top Downloads, User Rating, and Title sort options.