PlayStation 4 won't require a Plus membership for recording, streaming, and uploading game footage. Sony Worldwide Studios head Shuhei Yoshida confirmed that the functionality is in the system with or without a subscription, in response to questions following news that Xbox One's game DVR functions would require a Gold subscription.
Yoshida gave the responses directly to fans on Twitter, and his statements were later backed up by a UK spokesperson to Joystiq. PlayStation 4 will constantly record the last 15 minutes of gameplay in the background, which you can then edit or publish. You'll also be able to stream video of gameplay sessions live.
PlayStation Plus is required for multiplayer in non-free-to-play PS4 games. However, other online services, like accessing Netflix, do not require a subscription.