How important is teamwork in this game?

Is there friendly fire? How well are the classes complimenting each other? Are there any obviously broken skill combos yet?

No friendly fire (it would be quite annoying in Hardcore ^^; )

There are some passive keystones which may provide some combo feeling, but not much...

Elemental Equilibrium: Enemies you hit with Elemental Damage gets +30% res for this element, and -20% for the other elements.

Conduit: share Endurange, Frenzy and Power charges with other members.
(those charges gives bonus like attack speed or damage reduction, you can get 2 max without tweaking your passive tree)

If you were thinking about something like Guild Wars 2, nope.

edit:
I'm also playing marauder with a friend who play a witch with minions, it's always nice to have some meat shield, even for a melee class.

Just thought id mention on the subject of grouping up, the difficulty and the drops both increase

also because the different stats get different debuffs it can b very favorable to have several different players in a group so u can handle each situation using the apropiate debuff where needed =)