I agree with the other answers that mutual respect and shared goals are important. However, no-one (at the time I'm writing this) has commented on what I think are the two most vital factors: 1, each team member should have a designated role or responsibility, and 2, there must be a team leader. To me, that's the key.
It's fashionable to say there's no "I" in team; and teamwork ceratinly demands an element of egalitarianism, but it's equally true that 'motion isn't progress'. Vast amounts of time can be wasted on discussion that just travels in a circle. Somebody has to be responsible for channelling, and directing the team input if anything is to be achieved.
eg; in her answer, duffsmom has said "The ideal illustration of teamwork would be an orchestra. No one instrument makes the music but rather it is all of the instruments working together to make one beautiful sound."
I'd say; not without a conductor.