For the record, I have only seen the first season of this series. However, the fact that it only picks up and becomes consistently good-or-great about halfway into that season leads me to believe that future seasons will be of the same or better quality (I at least have reason to believe that this is true of season 2, but that's according to other opinions).
Anyway, this isn't really going to be a review but scattered thoughts on why I love this series so much thus far. I have no prior allegiance to Batman, and would not even consider myself a Batman fan as this is the first and thus far only Batman endeavor I've been a fan of, so it is not some inherent inclination to love all things Batman which makes me enjoy this series.
I think one of my favorite things about it is that the best episodes are presented so cinematically that each is like a mini movie - a term you will hear often on the DVD special features as a major aim of the producers, writers, and directors. Now I must define "best episodes." Because Batman is a superhero (and because of those pesky censors), the audience can be assured that neither Batman nor any other characters will die in any episode. That being the case, episodes fail when they attempt to dramatize some pathetic, uninvolving battle when the outcome is certain. The inverse of that would be the character driven episodes, and these, when done properly, become the (numerous) diamonds in the rough.
Take, for instance, "Heart of Ice": right down to his name, Mr. Freeze seems to be purely a gimmick. Indeed, he was probably conceived as such by whoever invented him in the first place. In the hands of scriptwriter Paul Dini and Producer/Director Bruce Timm, he becomes a tormented character with a very definite motivation. His ice gimmick becomes a symbol for his frozen emotional state, as he claims to feel no emotion... yet Dini also realizes and addresses the implications of such a character, because in the end it is revealed that the facade of the cold, emotionless Mr. Freeze actually hides one of the most emotional (sorry I keep using that word, but I'm too tired to think of a better one or look at a thesaurus) character in this or any episode.
I would say that if you have never seen this series, and you want to see a good example of what it has to offer, Heart of Ice would be a good place to start (Season 1 Disc 2, by the way). If it is your first episode, hopefully it will not be your last. I watched them all in chronological order, so maybe my appreciation is a bit heightened by the contrast with some of the earlier, lesser episodes, but I believe it is a great piece of work by any standards.
Other highlights in season one: On Leather Wings (great for a first episode), Two Face (if not an episode-to-end-all-episodes, it represents a step in the right direction for the series), Beware of the Gray Ghost, Feat of Clay, the Clock King, Appointment in Crime Alley, Mad As A Hatter (uses elements of Alice in Wonderland without ever seeming cheesy, and indeed it's surprisingly effective), and Dreams in Darkness, the last episode of the season that is probably the most polished as well.