As of the Xbox Live Spring Update (16 May 07 roughly) many people have been banned from Xbox Live.

Why you might ask?

Because they were using a modified Xbox 360. Many people do what is called a Firmware Flash to the DVD drive in their Xbox 360. Firmware Flashing allows the DVD drive to read burned copies of Xbox 360 games. Microsoft realeased the Xbox Live Spring Update with a way of recognizing that the DVD drive has modified Frmware.

Why should you care?

Because there will soon be, and probably already is, an influx of Xbox 360's on eBay. Most likely due to the Console being banned from Xbox Live. The console itself is linked to the Banning, not the Gamertag. If you are looking to buy an Xbox 360 on eBay in the near future, ask the seller if it has been banned from Xbox Live and be sure to pay by PayPal in case they lie. If you do get a Banned console, start a PayPal claim and hope for the best.