The Xbox One will come with a 500GB hard drive, and while that sounds massive, we all know how quickly those large hard drives can fill up. With the Xbox 360, you could replace the smaller hard drives with larger ones, but unfortunately, that's not going to be the case with the Xbox One.
Engadget spoke with Albert Penello, senior director of product planning at Microsoft, after the press conference, and he confirmed that the hard drive cannot be replaced this time around. However, Penello did confirm that the Xbox One has a USB 3.0 port that can be used for external storage, and such storage can do anything and everything the internal storage can do. In addition to transferring your saved games off the internal storage, you can also install games and download games/movies/etc. to the external storage.
So don't get too upset about this development. You can have plenty space for your downloading and storing pleasure.