In this post, I mentioned Twee60.com. One problem with Twee60.com is that it only does a rudimentary amount of filtering. (It only filters duplicates.) For games that change the Xbox Live status often, this will still cause a lot of Tweets to be created.
raptr is a site that does a better job at broadcasting Xbox Live status on Twitter. Instead of posting a status every n minutes, raptr will post a message, like "paul just started playing %s", when starting to play a game. In addition to sending statuses when playing games, it will also send messages when you get achievements. Raptr also supports gaming systems other than Xbox Live.
Here is my profile on Raptr: