Social features play a huge part of the community building aspects of virtual pet sites. They set the tone of the game. Without a forum, messaging, or a chat system, players won't be able to communicate with others.
Every social feature is important and I don't think you can build a game without them. I'm a huge fan of social features, but every player has a choice, and the freedom to interact with others.
Bonds and friendships are formed when there's social features involved, and that to me, is one of the most important things in regards to pet games.