Diablo 3 is, well, pretty much Diablo.
Gameplay is pretty much the exact same as the previous version. About the only new element is monsters sometimes drop health globes. It's an interesting mechanic because it sort of shifts your relationship with health potions a little bit.
There's also no real mana potions anymore. Resources either regenerate with time, or specific attacks build resources and other attacks spend them.
A lot of stuff got streamlined. Town Portal is now an ability (with a long cast time) instead of scrolls. Items are automatically identified. You pick up gold automatically. All your characters share gold, the stash, and crafting professions.
The major area of change is how abilities are given out. I think Diablo 3 is the final nail in the coffin for talent trees, at least as far as Blizzard is concerned.
Instead you get a series of exclusive choices. I.e. you choose one of 5 primary attacks (left-mouse button), 1 of 5 secondary attacks (right-mouse button), 1 of 5 defensive abilities, etc. You can also modify each attack with different runes that alter the attack. Like the monk has a spinning kick secondary attack. The first rune adds some fire and a knockback, and the animation changes a bit.
All of these choices are unlocked as you level, and changing your spec up is painless. I'm generally a fan of the series of exclusive choices idiom. I think the total possible number of combinations is just as large as with talent trees, and the total number of viable combinations is much larger.
There's also some interesting innovations in multiplayer. For example, loot is generated separately for each player, so there's no ninja'ing.
It's interesting to look at D3 in light of future MMOs, and think about what will get carried forward. I think the individual player loot is one element that will show up in future MMOs. Indeed, Looking For Raid is going to work that way in Pandaria. As well, many elements are shared across your characters, including gold, your bank/stash, and somewhat surprisingly, your crafting progression.
As for classes, they're pretty straightforward. The witch doctor is a bit weird though. I'm not sure what class I will play. Normally I just go with the knight/paladin archetype, but D3 doesn't have one. Mechanically, the armored melee fighter is the barbarian, but it just doesn't feel the same. I was thinking about the Demon Hunter, but like Spinks, I'm not thrilled with the high heels. Boots would have been just as sexy, and far less stupid. But otherwise, the Demon Hunter looks good, so I'll probably end up going with that.
In the end, this is Diablo. It looks, feels, sounds, and plays like Diablo. It has the classic Blizzard polish, attention to detail, and excellent performance on even somewhat older systems.