During the Sony E3 2013 Press Conference, Jack Tretton revealed a couple of features of the PS4 that were met with heart-felt cheers...
First, the PS4 will support used games, just as the PS3 does today. Also, there is no need to keep your console connected all the time. If you're interested in playing games locally, rather than engaging in multiplayer aspects, you can do so without connecting to the Internet.