Batman has always been my favorite superhero. This is not to say I haven't enjoyed other superheroes as well - I loved the old Superman movie with Christopher Reeves growing up (sad about his accident), and I loved the Spider-Man movies that came out in my adolescence (or at least the first and second - I wasn't such a big fan of the third). But my favorite hero has always been Batman.
This is also not to say that I've enjoyed every Batman movie I watched. I enjoyed Batman Begins immensely - more than any other live-action superhero movie I've watched, in fact. But I did not much enjoy the Dark Knight, not being a fan of Heath Ledger's Joker; and I don't really have much interest in seeing the third movie in the trilogy. My favorite presentation of Batman has always been the animated series. It's always been the most fun for me.
Part of the reason I like Batman better than other superheroes is that without special powers, he is much like an ordinary person. Of course, his alter ego Bruce Wayne is rich and famous, which allows him to have all sorts of cool toys and gadgets to play with. But without the extraordinary superpowers of a Spider-Man or a Superman, he has to survive on his wits, physical training, and (most interestingly to me) his detective skills. Comics often billed Batman as "The World's Greatest Detective," and in my mind, the character always lived up to this billing. He has an ability to solve crimes and get at the truth, in a way that few other characters can.
And part of the reason I like Batman so much is the cool gadgets and toys he can play with. Most of all, there is the Batmobile, which has always been my favorite car. How do you beat the sheer coolness and sexiness of the Batmobile? I've often wished that my car could do the kinds of things that Bruce Wayne's car can. Alas, it cannot, and I am left with dreaming.
As far as what sets this series apart from other films in the Batman franchise, it's hard to put my finger on it. Part of it might be that for a children's show, it can have some surprisingly adult themes. Batman has a much darker and more serious tone than most children's shows, and it does not shy away from depicting the urban underworld. It's sanitized and made more fanciful, but the sleaze and color of it is there, to a degree not seen in other children's programming. The show is just more dark and serious than most other shows.
And part of it might be that the series just has some great storytelling. I love the voice acting in it, I love the dark visual style of the drawings, and I love the development of the characters. Mark Hamill is my favorite Joker actor, and his performance has the right combination of humor and evil to make the villainous character work. And most of all, I love the good guys in it, from Batman and Robin to Alfred and Commissioner Gordon. The characters are compelling, and I've often wished that I had Batman's physique, money, and car. (Only half-kidding about the car part.)
Not everyone would like this series. But some would find a lot of fun in it. I also have used it for another purpose - practicing my Spanish. I watched the entire animated series (over thirty hours) with Spanish subtitles, and learned a lot about the vocabulary and grammar by so doing. No matter what language you watch it in, though, the Batman animated series will be one of the superhero classics for years to come, and I imagine I will be enjoying it well into my adulthood.
DVD Volume 1
DVD Volume 2
DVD Volume 3