Hey there, I know that there's probably nothing that the forum needs more than another set of beta impressions, so here's mine.
First, here's where I'm coming from: I'm someone who's played a lot of Diablo II, and while I love the game and think it's incredibly fun and hells of addicting, I recognize that it has a lot of flaws. When Diablo III was announced and throughout its development, there's a lot of things that I was hoping they'd address. At the same time, I love the feel of Diablo II and really wanted to keep feeling that. With that in mind, I'm going to start with things I liked, move on to things I didn't like, and then talk a bit about each class. I'm going to say a lot of bad stuff about Diablo II in here, and that's not because I think it's a rotten game, but because I'm focusing on differences between the games, and most of the differences are things that are improved in Diablo III - unsurprising with so many years to have learned from DII.
My actions feel like they matter - First off, as tons of people have spilled no shortage of ink about, the beta is very easy. It's not impossible to die if you're goofing around or playing with other people and you get spread out, but in general you can be pretty careless and survive. That said, the game does a much better job - even in the tutorialish beta - of feeling like my skills are making a difference. Diablo II isn't entirely a skill-less game, but playskill is dwarfed in importance by skill build and gear. "Skill" in Diablo II is generally about exercising more or less caution in different situations. Diablo III is a real breath of fresh air in that regard. Battles feel like they're won as a result of deftness with the game, rather than as a result of having enough lifeleech to same-attack a boss into the ground before I run out of potions. Again, most of the beta is no threat whatsoever, but I still get the feel.
Danger feels more dangerous - In Diablo III, when you're low on life and your potion is on cooldown, you're in danger. You don't have a dozen health bulbs' worth of potions to back you up. Again, as the beta is really easy this isn't something that comes up much, but I like when it does.
Monsters are interesting - I don't think it's an exaggeration to say that the skeleton king fight - occupying approximately the place Blood Raven does in DII - is literally a more interesting fight than any boss fight in Diablo II, except perhaps for Diablo himself. Even the relatively simple monsters in the first part of Act I feel like they're best handled in different ways.
Characters feel alive - In Diablo II, there's a handful of places (concentrated in Act I) where the character makes a comment about the environment or whatever. Diablo III expands on this hugely, especially once you get the Templar. The Templar has a ton of dialogue, including for places in the game that are before you get him during a normal playthrough, and I think his character is very well-realized. I'm really looking forward to meeting the other two followers. There's even a nice attention to detail moment when you re-run the quest where you get the templar when you already have him, in that Kormac treats the "new" templar as another member of his order and they chat a bit.
Screw you point saving - One of the most obnoxious parts of DII is that it's beneficial for nearly every build to save points, meaning that you're lame and boring for the first bunch of levels. That's gone.
More character sheet info - Thanks! Assuming that this info is correct, at least, thanks!
Lots of skills at once - I might be in the minority, but I found - even with just a two-button mouse - it very easy and intuitive to make use of all four skills I had assigned at once. It's hardly necessary for the beta - it's trivial to beat it with just any left-click skill - but I'm looking forward to non-awkwardly being able to make use of a lot of skills.
Optional difficulty through implicit challenge - This one's super duper clever. Now, the beta is easy. It's really easy. People with much DII or ARPG experience could just left-click through it with minimal danger unless they're very reckless. But the game has sort of built-in challenges that give you something to shoot for even when you're playing beneath your skill level. Things like trying to kill monsters with the environment, or kill a bunch with one shot, or kill a bunch in a row. I definitely found myself chasing after those things, effectively "challenging" myself in a difficulty area below my skill level.
Yay crafting - Crafting means that every blue item is an item I'm happy to get and gold is always great, because I can use those things to craft. Really digging the crafting system!!
You get to be your class from the get-go - From level 1, you're a wizard. You fight like a wizard. You don't fight like a low-HP stick-fighter who can cast a crummy fireball once in a while. It's baller! Almost too baller!
Skill interface - Ugggggggggghhhhhhhhh.......
The skill interface is the one single element of the game that I consider to be borderline unacceptable. It's awful. There's no excuse. Skills are sorted into only very vaguely sensible categories, meaning you have to hunt them down each time, a process that takes way too many clicks. Want to compare two skills by mousing back and forth between them? Tough. Click a bunch of times between them instead. Oh, and when you click off of a skill we won't remember what rune you had selected for it, defaulting to "no rune". Heavy rearrangement of your skill bar is just a giant pain. I knew about elective mode being the default before I got into the beta and thus knew to immediately disable it, but it's still a farce that that's a thing, especially given the arbitrariness of the skill categories. There's nothing about the skill interface that doesn't suck.
Reduced desire to build characters - I'm a strong example of what in Magic: The Gathering parlance is called a "Johnny" - someone who likes to use customization and build options as a creative outlet, to see out unusual combinations, to show people things they've never seen before, to express themselves through design. Consequently, one activity I really loved in DII - despite its limited effective customization options compared to a deckbuilding game like Magic - was trying to put together offbeat builds, poring over different options, and so on. For whatever reason I don't feel the same way about Diablo III, even though it has effectively a jillion times more options and things that interact with other in a jillion times more ways. I think there's some part of me that just sort of thinks "eff it, I don't have to worry about any of this now, I can just mash different skills around whenever". Don't get me wrong - I'm in favor of skills not being locked-in - but it makes it hard for me to dream about building characters because there's no actual building.
Barbarian - I had a lot of fun with the barbarian. All of the classes' attacks - with the possible exception of the Witch Doctor - feel like they have a lot of "heft" behind them, but the barbarian is the king here. I would even sometime smack a corpse around for a while just because I liked the way things flew when you hit them. With relatively few unnecessary-in-beta defensive, disabling, or support skills, the barbarian had one of the highest proportions of skills that I spent a lot of time with, and I have good things to say about almost all of them. Rage builds up at a rate that means that you get to use your rage spenders quite a bit, but not so fast that they're unlimited, which I really liked because it means that it's actually correct to juggle between a few different skills. (Not necessary, but technically best.) If there's a low point with the barb in beta, it's that a lot of early skills feel very same-y; it didn't really feel different when things were switched out.
Demon Hunter - For a lot of the beta I think the general mood has been that this class feels the weakest in the beta, and I'd agree. The blame I think lies almost squarely on the fact that the glass doesn't get a powerful, reliable area attack spell for quite some time, and since everything in the beta dies in one or two hits anyway, save the most powerful monsters, the ability to focus single targets down doesn't really matter as much. The class gets a lot of skills during the beta that aren't very helpful during the beta because survivability isn't much of an issue, and using hatred-spenders like Impale doesn't seem worth working into the rotation, since keeping track of your hatred doesn't seem worth it for what's going to likely be just overkill damage anyway. Rapid Fire feels satisfying against bosses, but until you get Chakram, the DH feels like a one-button class - and the one button is probably Hungering Arrow. (Chakram doesn't come until after the normal SK-beating level.) I hope the DH blooms a little more going forward. (I assume it does.)
Monk - The monk is a blast to play - probably overall the most satisfying. Even skills like Tempest Rush that don't have much role in the beta are a total blast to use. While, like most classes, the monk gets some support skills that aren't very relevant in the beta, the rest of his skills feel incredibly powerful. (Possibly because they are.) Deadly Reach might be the most potent spammable attack in the beta, and runed - you get the rune that makes it into multiple "forks" pretty early - it's a total beating, clearing packs in short order. Dashing Strike makes the monk feel really kinetic, and while I thought the knockback on Lashing Tail Kick would be annoying (given that Knockback is a very annoying property in Diablo II), it actually just feels like a lot of fun. The monk has a few small oddities - the strike area of some of his abilities is non-obvious, and the Thunderclap rune for Fists of Thunder (which teleports you to the target, at least some of the time), while very cool, is exceptionally disorienting at first because you don't always expect the teleport and then the whole screen shifts, effectively putting your cursor in a different place. Minor quibble on the whole, though.
Witch Doctor - Before I got into the beta, I thought the Witch Doctor would be my class of choice. It still might be, but not for the reasons I expected. More than any other class, I think that the Witch Doctor has to be played to be experienced. A lot of spells that just sound kind of weird, like Corpse Spiders, are a total blast to play with, and contribute to the (beta) WD's death-by-a-thousand-cuts play feel. You only get one pet - the zombie dogs in the beta, and they do feel very effective in the sense that the game gets much harder when they die. Without them or another control spell available, I'd be a little scared. (Grasp of the Dead serves a similar role just fine.) The dogs don't do much damage at all, but they're nicely beefy without being immortal. (They die super fast against the Skeleton King.) Based on my experiences, I'd be afraid to play a WD that didn't have any way of containing enemies.
The WD feels like it kills things a little slower than other classes. I'm not sure if his actual DPS is slower, but part of it may be that many of his skills have some form of delay on them - poison dart does some of its damage over time, which means that something can be about to die from the poison, but its body is still in the way to eat another dart. Corpse spiders has what's effecively a fairly slow projectile speed as the jar arcs through the air, and then the spiders bite, and then the spiders bite again. Things like this mean that even if the WD's total damage output is pretty high, the monster kill time might be a little slower. (I'm much more likely to throw more Corpse Spiders than were necessary than to shoot more Magic Missiles than I needed to.) The Witch Doctor's third skill, Plague of Toads, is tricky to use and feels uncessary in the beta, since it mostly just overkills anything it does hit. This is especially true if you're using Soul Harvest, a spell that applies an extraordinarly large buff to the WD that makes it such that all your skills (except for the individual corpse spiders) tend to one-shot most enemies.
Another random WD tidbit - while, unlike the other classes, the WD doesn't have its skills split into resource spenders and resource regenerators, the "primary" skills all cost so little mana that they can be spammed almost forever (or actually forever, in the case of corpse spiders.) I never ran out of mana on the WD except when using Firebats, which drains it very quickly. It comes back pretty fast.
Wizard - This is the class I played the least of, but I still have a few thoughts. I was surprised at the "heft" the class had - the things you shoot out feel heavy. Of the three ranged classes, the Wizard was the one that felt the least reliant on having some way to keep enemies out of your face, simply because killing them first usually seemed to be an option. I want to reiterate that the class comes out of the gate spells blazing - this isn't DII where you're a stickpuncher for a few levels before you get to be a real wizard. Arcane Orb, which you get at level FIVE, is a real beating of a spell, capable of leveling big packs of enemies in a cast or two. It's fun to try to angle it to catch as many enemies as possible. I haven't seen much chatter about Wave of Force (as a support/defense spell, it's largely superfluous in the beta, especially given when you get it), but it's my favorite skill of the ones available in the beta. What can I say, it's just fun to make a bunch of skeletons fly backwards. And they do FLY - as with the monk's Lashing Tail Kick, knockback in DIII isn't the little sliding bump it was in D2 - you wing people throught the air.