I agree with gela, the Earl may look like an idiot, and sometimes act like one, but he is seriously strong. The Noah's are also really cool, especially ones like Tyki and Rhode.
The storyline is also something that is something that stands out and I really like the way Allen tries to save the akuma and tries to keep their existance equal with that of humans (Because there are some moral dilemmas facing different caracters in the manga). I also think that the Hoshino was really able to play out the dilemma's with Miranda's anti-akuma weapon really well. The fact that it can stop time and heal people but its only temporary (one of the reasons why Volume 7-8 are my favourites).
And yes, the action is cool.
Basically theres a lot of different reasons why I like D.Gray Man, and those reasons can be about the small things in the manga, like some of the funny interactions between Lavi and Allen or the larger things like the intense battles where the Noahs need to get their asses kicked.