You'll need to download a 300MB patch to access most of PlayStation 4's features. However, you'll still be able to play games out of the box. With over a million consoles scheduled to go out on day one, there's always a chance that PlayStation Network servers may be hammered. Thankfully, you'll still be able to play games and have the update the download in the background.
Sony Worldwide Studios president Shuhei Yoshida confirmed on Twitter that you'll be able to download the patch in the background.
Of course, you'll only be able to play games offline. Without the update, you won't be able to access PSN features. You also won't be able to play Blu-ray movies or DVDs, so while your PS4 is downloading the update, expect to play games. And, really, only play games.