To be fair, you will only have them as long as MS continues support for XBL on the 360. Once the new gen comes, odds are they will cut it, just like they did for the regular Xbox.
You mean five years after they released the 360?
They didn't just cut support for the original XBL, and as far as the console goes, they only did that because Nvidia was attempting to extort them, and they wouldn't go for it, so the GPU made by Nvidia became unavailable.
It is sort of difficult to manufacture a console when one of the major components is no long available because you refuse to pay extortionists the price they are demanding.
Also, if you have a working Xbox 360, that has the console license, support of XBL on the console has no impact on your ability to play your games on it.
R.I.P. Eve English (Feb. 12, 1968 - Oct. 13, 2010) Momma Eve, you will be missed.