Microsoft has confirmed that the Xbox One will not support an external harddrive at launch but will in the future. Xbox One units will ship with a 500GB internal harddrive that cannot be replaced. But at E3 during Xbox One's unveiling Microsoft said that an external USB 3.0 port will be available for a second drive.
However this feature will not be available at launch. "The future plan is for definitely to support external storage much like we do on the Xbox 360," Microsoft's Larry "Major Nelson" Hryb said during a podcast during PAX. "My understanding is that feature will not be there at launch because the team is working on some other things, but it definitely is on the list. I don't know when it will come in though."
Sony has confirmed that the PlayStation 4 will also have a 500GB harddrive, is replaceable but does not support additional external drives.