I know Blizzard has said they have no interest in releasing any new classes, but I think it would be fun/cool to round them out. Their main beef is that it's pretty clear what all the current classes *do* - a new class would have to do something, well, interesting.
Here are my thoughts on at least hero powers for each:
Death Knight - Freeze! (2) - Freeze a character. (JT: Frostbite - Freeze a character and deal 1 damage to it.)
Monk - Kung Fu (2) - +2 Attack this turn. (JT: Kung Fu Mastery - +3 Attack this turn.)
Demon Hunter - Stifle (2) - Silence a minion. (JT: Squelch - Silence a minion, then give it -1/-1.)
So with Death Knight, it would probably be a mix of Freeze Mage and Warlock - lots of Freeze stuff (is literally always able to Freeze someone), and has powerful things at the cost of self-abuse. Has weapons, obviously, probably at least one that Freezes. Probably a life steal ability or two.
Monk is basically the other side of the middle that Druid straddles with Warrior, which I think is probably balanced. I have no idea what kind of cards he should have, though.
Demon Hunter is always able to Silence - Taunts mean less to him, and he can make use of cards like Ancient Watcher and Venture Co Mercenary that otherwise come with drawbacks. Hell, he'd even like an Icehowl thrown in there. I do have one card in mind for him - Mana Burn, (3), Overload 3 of the enemy hero's Mana Crystals, and deal 3 damage to him.