According to a recent interview with Sony's president of Worldwide Studios, Shuhei Yoshida, in the latest issue of Game Informer, the PlayStation 4 will not be an always-online console. The reason for the console not requiring a constant internet connection is because of the differences in the reliability of internet services in different countries, with many locales not having up-to-scratch connections.
Did we consider [an always online console]? No, we didn't consider it. The main reason being that many countries don’t have robust Internet connections. It makes sense for people to have Internet connections to play online games, but for offline games there are many countries that we saw [that] do not really have robust Internet.
The issue of always-online game consoles is a contentious one, as there is a lot of debate currently surrounding the next Xbox, which may or may not be require a persistent internet connection depending on the rumors you read. The latest report, sourced from an internal email to staff working on the Xbox, seems to indicate the console won't be always online, although we won't know for sure until the console is detailed later this month.
Meanwhile, the PlayStation 4 is slated for launch in the holiday period at the end of the year, with more information to come at E3 2013 in June.