When I first got an Xbox 360, I programmed my universal remote *not* to turn the Xbox off when I was done. I was downloading a lot of games and TV shows from Xbox Live and didn't want to interrupt the downloads.
I mentioned this on Buzz out Loud and a fistful of people wrote in and called to remind me that Microsoft fixed that issue a while back.to activate background downloads.
Go to My Xbox
Choose system settings
Then console settings
And go down and select shutdown
Then select Background Downloads
And select Enable.
Now when you turn off your Xbox, downloads will continue in a low-power mode until the download completes.
Hope that makes your downloading on the Xbox a little more convenient.