WesternAnimation A must watch all around
Theory: Batman alone is tragic. Batman in a teamup is cool. Batman in a league: AWESOME. If Batman the Animated Series is the soul of the DCAU, where it first got its legs and took flight, here is where it grew up and became so much more. The depth and humanity displayed in full-length movies such as Batman: Mask of the Phantasm is here in most episodes (there are, as always, a few misteps. Hawk and Dove is one that stands out, mainly for being exactly the wrong kind of ridiculous.) Do you have a favorite character in the DCU? You'll probably get something out of them here!
If you don't know the DC universe, if you don't know Batman or Superman at all, perhaps you should start with Batman the Animated Series. If you do know them, at least a little, you won't go wrong by buying the DVD collection if you want a great action show with fun characters. Not for kids, but nothing more than PG-13 material. Thats my 2 cents.
WesternAnimation The platonic ideal of Batman stories
I've watched the series when it first aired 30 years ago, and I was a teenager. It blew me away at the time. I've been rewatching it now with my wife, now as a middle age guy, and it still takes my breath away.
We've seen a LOT of superhero adaptations since this show first aired. Some are pretty good, some are bad, some are more of a mixed bag. A few even have unexpected sophistication, like Joker and Logan, but Batman: the Animated Series is that unique case when the adaptation manages to distill decades of superhero stories into a sort of platonic perfection. It captures everything that is great about Batman perfectly.
Of course, not all episodes manage to reach this elevated plateau. There are a few misfires in there, but even most of the duds would be hits if they'd come from a lesser show. But about 80% or more of the episodes are incredibly good, and the best of the bunch are better than the comics themselves.
Yes, sometimes the rigid strictures of being a 20-minute cartoon show made for a general audience in the early 1990s are a bit evident. Even though some people are of the opinion that the avoidance of graphic violence actually elevates the show above some of the more bleak and gory Batman comics. Myself, I think the show would be even better if the rigid censorship imposed over mainstream animated shows of the time had been a little more relaxed : you still have a little too many characters falling into rivers, gassed, etc (this is particularly evident in the first season episodes that aired on Fox Kids; Warner was a bit more relaxed). But even with this added burden, Batman: the Animated Series still shines through.
The other shows in this continuity, Superman: The Animated Series and the Justice League shows are also pretty good (particularly the first season of Justice League Unlimited), but none of them manages to reach the perfection of Batman: the Animated Series.