I suggest getting a new hard drive. Mine is 250 GB so I never have problems.
I use to though when I was still rocking the 20 GB which sucked.

But then, I got a 250 GB 360 Slim and wapow, tons of Games on Demand + FFXI + plenty of space.
But yeah for the original Xbox 360, the HDD's are so cheap at Gamestop right now.