As somebody who spent most of the day yesterday on the sofa with his PS3 and PS4...
- First of all, this wasn't just the US. Europe was affected as well.
- Disc-based games were working fine all day on both consoles. I've seen FUD above suggesting that always-online connections may be required for these. They aren't. Certainly, MS wanted to do that until the 2013 E3 (and I'll bet Sony gave it a lot of thought as well), but it never actually happened. Single-player modes of disc-based games were fine all day.
- Providing the console you were using was set as one of your primary consoles, then downloaded games (including PS+ games) were also fine all day.
- Basic login was down at first but came back after a couple of hours. Barring a couple of glitchy periods, it was mostly up through the rest of the day. Cloud save functions were working whenever basic login was up.
- Online matchmaking also came online a few times during the afternoon, though never really for long enough for a proper multiplayer session.
- The PS Store and Account Management features were off until quite late last night, When basic login was up, trying to access these gave a "this service is currently undergoing maintenance" error message, implying Sony had taken them down deliberately as part of the effort to keep basic login and matchmaking working. With Account Management offline, the option to re-download content you'd already purchased was also offline.
As of this morning, everything seems to be fine again. What was interesting was how the timing (on a Sunday, and a Sunday followed by a public holiday in several parts of the world) affected both the Sony response (which in communications terms was extremely slow) and the media-coverage (which was virtually non-existent for most of yesterday).