Let's start with Priest which has been the weakest class in the game for far too long. Blizzard have tried to remedy this situation in each expansion, and mostly failed.
No surprise they're trying again, it seems by introducing a slew of new archetypes and hoping one sticks.
The most obvious one is a necromancer. With cards like Spirit of the Dead and Sand Drudge, Priests have the potential to summon armies of undead.
What's particularly interesting about this is that there seem to be several viable builds here. The necromancer cards combo with spells, resurrect even weenie minion buffs. We could potentially even see an aggro Priest build.
Priest also has a long-standing tradition of stealing cards from other classes. But, unlike the equally roguish Rogue that hasn't, as yet, translated into an actual archetype.
Princess Talanji is the card that makes this a possibility. She could also combo with various Discover effect cards in a Dragon or Taunt-heavy build.
Mage is also in the doldrums a bit right now after the nerf to its workhorse card Mana Wyrm. But while that shafted tempo based decks, control versions just about hung on in the meta. Those look to be getting a boost from new cards like Firetree Witch and Arcanosaur.
There's also a semi-new archetype on the horizon for the class. Players have tried Spell Power Mage before, but it never quite worked.
The classes' Spirit and Loa from this expansion, though, are clearly aimed at remedying that. They're ably supported by other cards like Pyromaniac and Daring Fire-Eater.
At the other end of the scale, Paladin and Druid are currently riding high in the meta. Fittingly, then, they don't get too many interesting new toys.
Spells and handbuff look to be the big things for the former, but it's hard to see them displacing the reigning Odd and Even decks for the class. The latter gets a slew of new Beast pets, but not enough to make Beast Druid into a workable theme.