Stemming fears of the always-online requirement still rumored strongly for the next Xbox, a Sony PR rep confirmed to Kotaku that: "PS4 games will be playable without an Internet connection."
I'm still hearing from at least one very good source who hasn't failed me yet that the next Xbox, codenamed Durango, will require an online connection, though that source isn't sure whether the console would tolerate spotty, dropped connections.
In an interview with Eurogamer at yesterday's big PS4 unveiling in New York, Sony's head of worldwide game studios, Shuhei Yoshida said, of PS4 gaming, "Oh yes, yes, you can go offline totally. Social is big for us, but we understand there are some people who are anti-social! So if you don't want to connect to anyone else, you can do that."
Sony is hoping that you would keep your machine online, though, so they can keep quietly patching games, updating games, sending games to you and all sorts of other stuff. This is a company, mind you, that painted a vision yesterday of a "psychic" online store that would learn your tastes and have the next game you might want to buy already downloaded to your machine before you even knew it existed—just waiting for you to click to pay.
Note: Last year, when we reported the PS4's codename—Orbis—we also reported that, while there probably wouldn't be an always-online connection for PS4, that we were hearing that users would need to register their games online. We're following up with Sony to see if that is at all part of the current PS4 plan. Even if it had been, things can change and we're trying to keep you as up to date as we can.
UPDATE: More relief... At a roundtable this morning, Sony's game studios chief, Shuhei Yoshida, told reporters that any requirement for users to register a game online in order to play it would be left to game publishers. Sony won't require that.