Mostly I watch Japanese anime; the shows that wash up on American shores, at least, have better plots, characters, and animation than the general run of American cartoons ... and many American live-action TV and movies, for that matter. In approximate order, here are my favorite TV or OVA series:
Admittedly, Utena is an acquired taste, and Excel Saga is too weird and shrill for some people; I'd recommend the others to anyone interested in anime. If you're not willing to spend 26 or 39 (or 13 or 6) half-hours on a series, I'd recommend the movies of Hayao Miyazaki (especially Princess Mononoke and Spirited Away), or Satoshi Kon (Perfect Blue, Millenium Actress) for grownups. (Don't try the movie versions of the above series; many depend on knowledge of the series, and some are just not that great.)
There are also some series which I wouldn't call brilliant, but which have their moments:
Notable series I'm watching right now (2004 Dec 2):
Also, I'm a subtitle snob. Not that Japanese actors are always better than American ones; the American V.A.s of Cowboy Bebop are very good. For me, I guess it's the "Speed Racer" effect: in order to match the mouth flaps, the English scripts add or change words. (Not that subtitlers don't edit for length as well, but at least they don't add words.) Plus I just like the sound of Japanese, and certain Japanese voice actors:
Note: I've listed names below in Western fashion, and only credits for series mentioned above.
Not that America doesn't have some excellent cartoons. However, since Americans are too grown up for cartoons (as opposed to Fear Factor and The Apprentice), good cartoons are rare, and seldom released to video or DVD:
Invader ZIM rocked: great production values, hilarious and subtly disturbing plots, off-kilter dialog, and the brilliant voice-work of Richard Horvitz (among many) as the title character. Unfortunately, it's the property of Nickelodeon, who didn't stop to think what the author of Johnny the Homicidal Maniac might create, and didn't know what to do with it once they bought it. At last they had the good sense to grant distribution rights to Media Blasters, who've released it to DVD in a funky-looking artbox.
Batman, especially in the post-Miller era, is one of the few superheroes I ever liked. The early 90's series used "dark deco" smart scripts, a sweeping musical score, and excellent voice actors like Kevin Conroy and Mark Hamill (Luke who?) to breathe new life into an old franchise. The same team went on to create Superman, Batman Beyond (a failed experiment in transposing Batman into the future), and most recently Justice League. Ten years later, the original series is tricking out on DVD. (Check out the movies, though, especially Batman: Mask of the Phantasm and the surprisingly good and dark Batman Beyond: Return of the Joker [Uncut].)
The animation is pretty spare, even stiff, but the real draw is the story of an alienated teenager appalled by the idiocy around her. MTV (which, like Nickelodeon, is a Viacom company) released only the first few episodes and the movies, despite petitions to put the whole series on DVD. The series is running on Noggin, albeit in a drastically edited form.
I'd also add The Powerpuff Girls to the list of good American cartoons, even though I don't watch it much anymore. I'd even add Aeon Flux; it's pretentious and the dialogue is just bad, but it's enthrallingly strange and occasionally inspired.
As far as movies go, about the only people doing anything interesting are Pixar, and they've left traditional animation for CG. Unfortunately, this has led a number of idiots in expensive suits to declare that hand-drawn animation is dead and CG is the Next Big Thing ... ignoring the fact that Pixar's real strength is well-written stories. Especially recommended are Toy Story, Finding Nemo, and The Incredibles.
And of course there are the classic Warner Brothers shorts. If anyone knows where I can find a copy of "Little Red Riding Rabbit" ("Hey, graaaandmaaaaaa!") ...
I never understood superheroes. OK, just for the sake of argument, let's say I have powers far beyond those of mortal men. (Stop laughing.) Maybe I feel a duty to use my powers for the benefit of humanity. But I would never, ever, ever dress up in skin-tight day-glo spandex with my briefs on the ouside ...
Still, there's a lot of potential in the medium. Anyone who thinks comics are necessarily for kids -- hello, Dallas D.A.s -- should really read Scott McCloud's Understanding Comics.
So I'm not a big American comics fan, except for a few non-superhero titles: Sandman, Bone, Strangers in Paradise, with an honorable(?) mention to Jhonen Vasquez's Johnny the Homicidal Maniac, Squee, and I Feel Sick. Also worth noting are Watchmen, V for Vendetta, Ben Edlund's original Tick, and other deconstructionist superhero series.
The Japanese don't have so many superheroes, so I'm more of a manga fan: Great Teacher Onizuka, Kare Kano, Blade of the Immortal (sort of). (Since I'm a big fan of Utena the TV series, I'm also buying the manga version ... which is kind of lackluster, sad to say.) Past favorites include Maison Ikkoku, Ranma 1/2 (which I'm behind on), and Battle Angel Alita (the original series; I gave up on the new one).