Eek the Cat was another one that, although very childish, the majority of the humor and references were towards things that only adults (or, at least those over fifteen) would be able to understand.
And who can forget Betty Boop?
I’m surprised that no one has mentioned The Critic. I LOVED that show, and it was an adult cartoon without a doubt. 
Just got “Rex the Runt” DVDs. Insanely funny! Aardman Animations. I’d never heard of Rex before, but bought it because I am crazy about Wallace and Gromit, Creature Comforts, the Morph Files, etc.
“The Maxx” was a great show that was based on graphic novels from MTV. Unfortunately, MTV has the rights to the series and hasn’t put it on video as far as I can tell. The graphic novels are out of print, and are so rare to find that you have to pay through the nose to get them in this day and age… such is life.
For anime that’s more for adults but has fun with the viewer, I’d suggest “Elf Princess Rane” on dvd Japanese language with English subtitles. Parts of the subtitles are actually sentences typed backwards, and they’re very entertaining.
Focussing on animated films which are not for kids:
Princess Mononoke: masterly ecological fable by Miyazaki. On my personal top ten films list(including live-action)
Only Yesterday: a charming story about a 27 year old woman with episodes from her childhood ,at age 10, told in flashback. Directed by Takahata who is Miyazaki’s colleage at their Studio Ghibli
Grave of the Fireflies: Also by Takahata. I haven’t actually seen this but it receives near-unanimous rave reviews. It’s about a small boy and his sister trying to survive in war-time Japan.
{b]Jin-Roh Wolf-Brigade**: an noirish thriller about a Special Force agent in a fictional post-War Japan.
Each one of these films is a different genre. Each one of them is comparable to the best live-action films in the genre. If anyone has any doubts that animated films can be a mature artistic medium these films should remove them.
There are 10 very short web only episodes of The Critic available at Atom Films. It was basically Lovitz and some flash animators. They’re ok.
Fantastic Planet was more a Czechoslovakian movie which was supposed to be trashing Communism. Although when I watch it I can’t help feeling like I’m watching a movie about a 19th Century British eplorer. Perhaps the guy from The Time Machine or something like that. Mostly from the way it’s narrated.
I’ll add the early Rugrats episodes. You might think they were about babies but it was really about friendship and adventure and the occasional death colored by naivete. And also the Stu (the dad) Pickles story lines. Kids might just see a weird adult there but an adult would see much more. I think most American animators put things in that are deliberately over the heads of most children for the enjoyment of themselves and for other adults.
I’m going to post out-of-character and not mention anime for a change.
I’d like to mention, however, that HBO Animation put out a very good (once you get passed the first season, at least) Spawn animated series. Very dark, had Spawn voiced by Keith David, and was gory as hell.
One of my old college roommates also seems to think very highly of The Iron Giant, but I can’t really comment on this, not having seen it myself.
I’ve seen it. Made me break down & actually sob for these kids.
It’s a hard movie to cope with.