As I was saying, if you enjoyed the animated series from the 90's or the Tim Burton style of dark/brooding atmosphere, you'll love this animated movie. I don't want to ruin the plot for anyone so I'll just say what I think makes this movie so good without giving away too much. In "Under the Red Hood", Batman is portrayed as a hybrid of the dark knight from the kid friendly "Batman: The Animated Series" of the 90's and the portrayal shown in Tim Burton's "Batman" from 1989. Both Batman and Bruce Wayne are portrayed perfectly by Bruce Greenwood. All of Batman's gadgets and vehicles (including the Batmobile and the Batwing) all very closely resemble 1989's portrayal while also blending elements of the animated series. The Joker appears in this a lot and is again a hybrid of Mark Hamill and Jack Nicholson's portrayals of the Joker and the blend is superb (although the new voice may take some getting used to at first). Nightwing appears here and his outfit and demeanor is much less out of place than Robin but he can still kind of make things campier than they need to be at times (luckily, he isn't a main character and isn't featured much). Robin is a secondary character yet he is the basis of the story (I won't lay out the plot except that this involves Batman's failed training of a second "Robin"). I love the fact that this movie is PG-13 because it allows the story to be told in a way that it never could have if it were targeted to a younger audience. The reason it got the rating is that people die in this (sometimes brutally), they are tortured, there is more profanity, more talk about drugs and in-depth details of organized crime, and probably the fact that it's just much more bloody and dark. This movie has very few flaws though and I would rank it up there with some of the better live-action Batman movies (not to mention the superb "Mask of the Phantasm").
For die-hard Batman fans, this is a must buy.
For fans of live action Batman movies, take a look at some of the animated series shows or movies first.
For fans of the animated series, be warned that this is much more intense than what was released in the 90's or targeted to children back then with the straight to movie releases.