Barbarian - Rage. Builds up on hitting and being hit. Also has some skills with cooldowns that can generate it spontaneously (iirc, perhaps only 1?)
Witch Doctor - Mana. Same old same old, from memory.
Wizard - I believe it's called Arcanum now. Maxes out at 100, but nothing much more known about it (afaik)
Monk - Spirit. Generated through use of combo techniques (and some theorise that it may end up being generated in small amounts through normal attacks, too. But this is conjecture/suggestion). Expended through use of non-combo moves.
Demon Hunter - No news currently.
Did I get any of that right, for what we currently know?
Barbarian is Fury. Same concept, though.
Wizard is Arcane Power. It's like Mana, but is capped and doesn't increase as you level, but it has a higher regen rate than mana. The devs said this resource might change.
"If anyone needs me, I'll be in the Angry Dome." - Prof. Farnsworth
The acronym of my name is also my favorite poet. Call me Poe.