Batman: The Animated Series was absolutely amazing when it first came out in 1990s and still today it stands as an amazing program. It's a show that you don't even have to be a fan of superhero stories to enjoy because it did everything so well.
The original Batman: The Animated Series had the perfect theme music and that amazing art decco style which gave it a fantastic stylish look, with a lot of nice Noir elements. The show was darker than your average kid's fare but it still maintained a sense of fun and excitement. With Batman, particularly in the early years, it was all about the big story, the big moments.
The things that stand out about the series are episodes like, "Joker's Favor," "The Cape and Cowl Conspiracy," "Heart of Ice." These are gripping and exciting stories that really succeed in entertaining all ages while being intelligently written.
Harley Quinn was introduced in this series and has become vital part of the Batman mythos and their version of Mr. Freeze was stunning and heart breaking.
In my opinion, the later episodes just weren't as good, but still even those had some gems like, "Judgment Day," "Joker's Millions," and "Mad Love." This series also spun off several successful movies.
Batman: The Animated Series remains one of the most influential series (of any sort) ever and there's a good case for this being the best. Why I think another series was better than this, I'll save for when I talk about the greatest Superhero Animated series of all time. For now, we'll just tip our hat to Batman.