Board Thread:Questions and Answers Forum/@comment-6941549-20140907201617/@comment-4303374-20140907203053

You must have an internet connection to actually play the game.

However, in order to compete in Raids, Strikes, Public Events, the Crucible (PvP), etc., you must have PlayStation Plus/Xbox LIVE Gold.

I would recommend PS+/Gold, since, without them, you will be missing out on huge portions and elements of the game; but no, you do not need PS+/Gold to actually play.