Microsoft has reportedly started to take action and a no tolerance policy towards gamers running modded Xbox 360s by banning them all from Xbox Live for “inappropriate behavior like hacking or cheating” as it violates the console’s Terms of Use.

"We have stated in the past that customers can only enjoy access to the Xbox Live community through the use of a genuine, unmodified, Xbox console and we will continue to enforce this rule to ensure the integrity of our service, the protection of our partners and the benefits of our users."
The ban from Xbox Live is effective on the console only, so users will still be free to access the service using their account on an alternative unmodified console. Although Microsoft is claiming to be preventing cheating in games, most likely this measure is focused on preventing piracy, and you can’t really blame Microsoft for that.