Right now, the party set up is pretty fluid. All that's required is a tank, a healer, preferably a secondary healer whose first job is damage, and everyone else piles in with lots more damage. Right now, that means that the really high-level stuff demands a warrior, because no one is better at aggro management. Other than that, priest is the preferred primary healer, but a suitably-equipped or talent-specced druid or shaman can fill in without too much trouble. (The general agreement, if a group takes a druid, is to find a shaman or pallie for rez purposes and back-up healing.) For the rest, you can have whomever and generally do well. Duplicates aren't bad, though too many might be. The point is if you have 1 warrior and 1-2 good healers, the party can handle things if they're on their toes. In practice, this seems to not QUITE be the case; most people still aren't terribly sure about including a hunter in their group, from what I've been hearing. But the druid and the warlock, classes that were once shunned, are now finding more acceptance. This is very healthy.
WRT the "required" warrior: Blizzard has said repeatedly that they're looking further into aggro management, with the goal of making Druid-bears and Paladins viable tanks. I wish them luck-- it'll make things more interesting.