John Gaudiosi at PCWorld interviews Bungie's COO, Pete Parsons, about Bungie's new game, Destiny. In the interview, Parsons again confirms that an element some fans were worried would be omitted is in the game-- namely, solo play:

We want players to tell their own stories. We’re going to give them the ability to customize their character, and their experience. Then they’re going to go on epic adventures with their friends. You can play Destiny solo, but we believe that everything fun to do in Destiny is more fun when you’re playing with friends. It’s that unpredictable human element that will create the most important moments in Destiny.

The game may need to be online all the time, but it looks like you'll have the option of playing by yourself if that's what you want.