I know this thread is old, but it's literally this topic that got me to sign up for an account here because I really love talking about 'Dark Knight' so much.
As for what makes it so special, there are a ton of reasons. Two of which, I don't think I need to cover. One, the topicality of the film, which Tacit Ronin really covered in his reply so long ago. Two, being Heath Ledger's performance which I think has already been acknowledged plenty in this thread.
So the two aspects I really appreciate about the film that I think deserve more praise are, first, how much the film really gets and appreciates the source material. As a Batman fan, I love that. Second, it's a movie that tells an extremely satisfying character-driven story that really examines Batman and what it means to be a hero.
So, first, the source material thing. I love that this film really is so firmly rooted in the Batman comic books and takes the effort to truly understand it's characters and what their important, defining aspect are.
A lot of the TDK-backlash includes this notion that Nolan didn't really appreciate the comics and it's always backed up by some hogwash example overly focused on a surface level detail like how Joker's skin wasn't permanently white.
Ok, so let's look at that: Yes, Joker didn't fall into a vat of chemicals and come out looking like a playing card. But if we are honest, we all know that Joker's Red Hood origin is the result of silly comic book trope that we all take for granted now.
Nolan, however, had the insight to really look at Joker's character and origin and take the important bits and leave the baggage that would drag down the film. What is important about the chemical bath aspect of Joker's origin story? Well, it's that he suffers a disfiguration of some kind that makes him look as crazy on the outside as he is on the inside. The 'Glasgow smile' covers this perfectly. It's a Joker related disfigureation, but not one that requires a real origin story. It fits into Joker's role and character in such a way as to not detract from his role in the film but still provides the basis for him to be the Joker and not some other villain.
You can't get there if you don't respect the character in the first place.
Besides just respecting the characters, the film really does look to the Batman mythos for it's stories. And when it does so, it takes the essential, important themes and tries to adapt them for film and improve upon them. 'Dark Knight' is the 'Killing Joke' done far better than the comic book does it. It takes the important themes (how close each one of us might be to becoming our own Joker and the Batman/Joker relationship) and does away with the weak parts (Joker's rather uninspired origin story).
The same can be said for 'Long Halloween', which is my favorite Bat-book story arc, personally. (I picked DarkVictory for a name based on the not-quite-as-good-but-still-awesome sequel because it sounds like a better username than 'LongHalloween' does). TDK does 'Long Halloween' even better because it takes that important theme (what are the repercussions for Gotham and Batman when the supervillains begin to take over the underworld previously run by traditional organized crime?) but does away with the somewhat meandering serial killer subplot which was an important hook for the original serialized storytelling but far less important for a standalone film.
Then there is the character driven story. So many people kind of miss the Batman character arc and think this movie is about Harvey Dent (or their distracted by how awesome Heath Ledger's Joker is), but some of that is the beauty of Batman's character arc: It's built so well into the heart of the film that you almost take it for granted yet it makes the film great.
Batman here isn't just a brooding dude who kicks a lot of butt, has a killer costume, and drives an awesome car that sits around in his study waiting for villains to show up to give him something to do.
Batman has a goal at the beginning of this film and he believes he's almost there. The goal, however, is unrealistic and he doesn't appreciate the sacrifice that his quest will truly require of him.
At the beginning of this film (and this is a theme carried over from 'Batman Begins'), Bruce wears Batman like a shield. 'Batman has no limits'. He believes that he can use Batman to effect the change he wants in Gotham, get rid of the mob, find the right guy to take over the problems, and then drop the cape and cowl marry Rachel and live happily ever after in a city his parents would have loved. The end.
Meanwhile, he is oblivious to the fact that being Batman is slowly invading his soul. He's become obsessed with watching people. He builds a machine that spies on everyone. He misses the fact that he's pining after a Rachel he doesn't really love (or even truly know anymore) and missing the fact that she's obviously in love with someone else. He thinks he can compartmentalize his life and that by using 'Batman', he'll somehow be able to emerge on the other side unscathed as Bruce Wayne when somehow he is able to win his war.
All the while, the evidence is mounting that this isn't possible and it comes crashing down on Batman when the Joker is able to hurt him personally by killing Rachel. Alfred, who's been watching the whole time, says it best. 'You didn't think there were going to be casualties?'
This culminates in the final confrontation. I mean, it's pretty amazing when you think about it. The final showdown in 'Knight' is almost all dialogue. It's not a climatic battle with a hundred buildings blowing up. Yet, when Batman makes the choice to sacrifice his name and Gordon gives that speech to his son that could come across hokey in any other film, you still want to stand up and cheer the moment that pounding beat booms across the speakers and the credits start to roll.
Why? Because the film builds to this conclusion. The ending could be considered tragic in many ways. Batman finally, truly accepts that the Bruce Wayne he thinks he wanted to end up as is gone. He's given in to a lonely, painful, dark life as wanted vigilante. But because the movie has been building to this moment, because we've lived it alongside Batman, it's a heroic sacrifice as powerful as any giant fight scene could possibly be.
Man, I'm getting goosebumps just thinking about it. I could probably go on even more about some of the little things that 'Dark Knight' gets right (because there is so much more) and now I've got a giant urge to just pop-in my Blu-Ray copy but I need to go to bed now and I probably shouldn't watch TDK so shortly before I'm going to see 'Batman v Superman' as I'd probably just be setting myself up for disappointment.