According to joystiq, every mode in the game is played in groups of 3. Even multiplayer. wow
http://www.joystiq.com/2014/04/28/video-preview-destiny-wears-its-halo-with-pride/
Update:
As Parsons explained to me, players are free to tackle the campaign alone or with two friends. Every mode is played with groups of threes, incidentally – even adversarial multiplayer – as Bungie feels it offers the best balance for the three available classes. Each mission contains both private and public spaces, meaning some areas are dedicated solely to your three-man team, while other areas will be filled with additional players.
http://www.joystiq.com/2014/04/28/video-preview-destiny-wears-its-halo-with-pride/
Update:
There are several modes featuring more players that we've already talked about. Raids are a six player activity that will always be in parties comprised of your friends. Competitive multiplayer is not capped at 3v3.