Cromartie High School
Jungle Wa Itsumo Hale Noche Guu

I haven't actually watched it, but maybe Super Milk Chan Show.

I've seen all 3 of those.

Cromartie is awesome.
Second one's english localized title is Hare + Guu, which is far easier to remember. It's really amazing and completely hilarious.
I kinda like Milk Chan I guess, so long as we're talking ADV's 'americanized' gag dub verison.

Of course, Cromartie and Hare + Guu actually have continuity, but it really doesn't matter much with those. They have about as much continuity as your average sitcom.

Could I mention Excel Saga? It's got continuity sure but it's just so off-the-wall and completely nuts.

I want to mention Slayers, even though it actually has an "epic" overarching plot (well several of them) and definitely has continuity, but it's a parody and is comedic far more often than not. It's kinda like the anime equivilant of Terry Pratchett. Got like 5 seasons worth of episodes and a shitload of movies, OVAS, etc.

Oh, you'd have to watch it subbed since as far as I know it's still not been picked up for localization, but what I saw of Sayonara Zetsubo Sensei was really fun.

Shin-chan
Cromartie
Bobobo-bobo-bobobobo
Ping Pong Club
Jungle Wa Itsumo Hare Nochi Guu
Sayonara Zetsubou Sensei
Panty and Stocking
Pani Poni Dash
Azumanga Daioh
FLCL
Magical Shopping Arcade Abenobashi
Kamen no Maid Guy
Maria Holic
Excel Saga
Gintama
Yakitate! Japan
Sexy Commando Gaiden

There was this one that was so F-ing bizarre I can't begin to describe it. It was called"Super Milk Chan" You want no story? Check! No epic resolution? Check! Utter insanity? Triple check! Warning, it's very surreal and can get vulgar.

What about American humor? Is it funny to the Japanese?

Can someone give some examples of jokes that are funny to a Japanese but not to others?

Excel Saga was mentioned, and I quite liked that one. No continuation between episodes that I remember, just a bunch of random humor. I can see the main character's voice driving some people from watching this, but I enjoyed it.

FLCL:
The entire series is pure insanity. The best way I can describe it is this giant robot with a TV head comes out of a 6th graders mysteriously appearing horn, while the nurse-imprsonating Hara Hara Haruko rides around on her motorcycle beating up other giant robots with her Rickenbacker 4001 bass guitar. Other crap happens. Animation style is very psychedelic driven.

You also might like Hetalia, unless you're not into the ocasional homosexual gestures. You'd really hate the fan porn if that's the case.

As a side note, I'll be that "other guy" who strongly suggests Cromartie High School.

Great Teacher Onizuka (GTO) is pretty funny. Though it does deal with some serious themes at times it definitely doesn't take it self too seriously for the most part. I love that series!

FLCL is crazy yes but I'm not sure it fits the criteria here. It is a basically one short story arc.

I'll also just drop this here as well.