In July 2007, Microsoft announced they would be extending the manufacturer's warranty to three years on ALL XBOX 360 consoles worldwide for consoles which have a "three red lights" error (the first three of four rings are red upon starting the console).  This is wonderful for everyone who has bought a 360 from a retail store, however this warranty (AND the standard one-year warranty) is INVALID for anyone OTHER than the ORIGINAL PURCHASER.

from hxxp://www.xbox.com/en-US/support/systemuse/xbox360/resources/warranty.htm
under G. Additional Conditions
"This Limited Warranty applies to the original retail purchaser only and may not be assigned or transferred. However, some jurisdictions extend the protection of implied warranties to subsequent consumers and therefore this limitation may not apply to you."

This means that if you bought the 360 USED, you will NOT be entitled to any warranty, even if the Microsoft security sticker is intact (unless you live in a state that forces warranty transfer by law).  It does not matter if it was gifted to you, they still will not legally be required to honor the warranty.

Note: You may still be able to get around this if you have the original purchaser's name, the city the console was purchased in, and the store it was purchased at, when you contact customer support.

Be careful when buying secondhand 360's from anywhere, as the warranty will likely not be valid, unless you are lucky with customer support and get them to change the entire registration information that is automatically entered into their system by retailers [like I was able to :-), but only once].  Of course, the red light repair service costs have plummeted significantly after the warranty announcement, so you can always have a third party repair it (how many times it will break again, I don't know).

Thanks for reading this, hope this saves you from a bad transaction!