Xbox One's game DVR — the ability to record and upload your gameplay footage — requires an Xbox LIVE Gold subscription. This is according to the official Xbox LIVE features page which was spotted by One Hit Pixel. Microsoft later confirmed the requirement to the website.
In addition to game DVR, Xbox LIVE also enables its Gold subscribers to enjoy Skype and Smart Match multiplayer matchmaking on the Xbox One, and is required to play games online (on either the Xbox 360 and Xbox One).
Comparatively, the Xbox One's competitor, the PS4, allows users to record and upload up to 15 minutes of footage without a membership to PlayStation Plus. Not like it really matters all that much anyway because it turns out your going to need a PS Plus subscription in order to play games online on the PS4 now.
So really, regardless of platform preference, you're going to need to pay for some sort of subscription in order to get the full entertainment experience. Do you mind paying the $60 yearly membership fee for Xbox LIVE Gold?