Batman: Mask of the Phantasm (1993)
Dirs. Eric Radomski + Bruce Timm
MotP was the first film in the DC Animated Universe (TAS). The excellent voice acting, dramatic noir lighting, stylistic art deco designs, and Shirley Walker music all help elevate the work beyond a typical PG rated animation of the era.
Bruce isn't just an angry orphan fighting against a world that he feels took something irreplaceable from him, he's a flawed dark avenger, suffering emotional conflicts as he weighs the lure of a normal, loving relationship against an earnest vow to protect others from the pain he weathers. He's fully aware of why he does what he does, but finds reasons to justify it. I can relate to that. I'm sure we all can. (Except for the dressing in tights part?)
There's been dozens of Batman films since its release, but MotP is still the best that I've seen.
Don't be put off by the CGI opening that takes you thorough a sprawling Gotham skyline. There's an occasional use of CGI throughout the rest of the film, but mostly it's traditional hand-drawn animation, and is all the better for it.