The thing that seems to clog most people's minds is this: Dungeons and Dragons, the
original, Dungeons and Dragons, was not about deep and involved storytelling. It was about a group of people using their characters as pawns in a maze trying to escape while getting loot and avoiding or killing monsters.
As the game grew older, people began to add other stuff to it. With each successive edition, people added more and more to make the game resemble the other games out there - for instance, as telling
stories became more and more popular (curse you White Wolf!) the editors and writers of DnD tried to emulate them by making things more story-riffic.
3.* came along and tried to turn the whole thing into one system to rule them all. Unfortunately, it did a crappy job of doing anything more than what DnD was originally intended for: kicking ass, killing monsters, gaining gold. And yet people tried and tried and tried.
The 4th edition folks said, "y'know what? Screw that. We'll kick this thing old school" and removed all of the legacy materials that were simply trying too hard and made DnD better at what it already did the best: kicking monster ass, escaping mazes, and gaining gold. Possibly, they would save the world while they were at it.
So you have to approach 4e with that goal in your head. 3.*e went for immersion and "storytelling"; 4e went for gaminess. 3.* wanted everything in the world to make coherent sense. 4e said, "screw that, I'm turning on an action flick! Look at that guy dodge sideways with two pistols while doves fly behind him! That's awesome!"
4e wasn't meant to be anything more than what it is. It's not a game of deep and involved storytelling or world emulation. You can do it if you want, but that's
your call. The main motivation was to provide a roleplaying game that let you pretend to be an elf kicking ass in a pretend world. If you want a whole world simulation, there's 3.*. If you want dark and tragic tales of boo hoo, go play Exalted. If you want to shoot people in the face....

But if all you want is to sit down with some friends and kick a dragon's and its minions' asses, DnD 4th edition is here, with open arms and a dumbass grin on its face. Maybe it's too miniatures for you. *shrug* Maybe you want world simulation. *shrug*. Maybe you want tragic tales of boo hoo. *shrug* That's not what 4e was built for and yelling at it because it doesn't "do" what you want it to do is really screaming into the wind.
What I love about 4e -
+ A world that was built to resemble classic Dungeons and Dragons. One of the major inspirations for the 4e guys was
Keep on the Borderlands. The world is dark. Towns are scattered. Empires crumble. Monsters are everywhere.
+ The base campaign setting is both its own thing and an homage to earlier editions. Not only was Keep mentioned, but the Temple of Evil, Orcus, Vault of the Drow,
spelljamming, planehopping...all while the main assumption being that the characters are heroes and will go out and make their mark on the world.
+ Ease of use.
a) It's easy to make a character that is gameable. Not
optimal; some people are always going to find X better than Y no matter what, but a lot of the creation "traps" that plagued 3.*
as a design goal are gone and you have to actively work to make yourself suboptimal. I created an elf paladin of the god of Knowledge with a knack for history and language and he could still kick just as much ass as the guy who took feats that made his lay on hand or smite abilities better.
Someone also mentioned that race meant nothing: well, race really did nothing in 3.* either. In 4e, when you pick your race you not only gain skill and stat bonuses, you also gain access to racial feats and powers that will increase with level as you as you adventure.
b) It's easy to set up for. Encounter creation: figure out the average of your party level, take that xp total, and use it to "buy" monsters out of the Monstrous Manual. Adjust for party size, party ability, and terrain (which is a big factor in 4e).
c) The monster stats -
3.*e versus
4e.
d) Ease of starting where-ever the heck I feel like starting. Want to do an epic campaign? Pick race, class, adjust your stats and skills using the chart in the back of the DMG, pick out a paragon path and an epic destiny, pick out three pieces of gear - one higher, one equal, and one lower to your level, and money equivalent to another equal level item, and you're good to go.
+ Support. While I don't have a DDi subscription yet, I do hear it's worth it. They come out with playtest material for fan look-over, new classes, new powers and variations, new items, all sorts of interesting stuff. Dungeons been all right, not as good. And they've got the character builder and encounter builder which is getting all sorts of positive reviews from players.
Plus, their published material has apparently been pretty good and they've been putting a lot of effort into getting out to the fans. Again, they're crossing the culture by inviting the Penny Arcade / PVP folks and Wil Wheaton to do podcasts for them, they've got Shelly Mazzanoble to outreach to the interested female gamers, they set up demoes at local shops and have an active interest in PAX. I mean, they're really invested in getting people to try the damn game.
And thus ends my long winded, lunch hour eating post