I like non-comedic animes that end up being funny sometimes (ex. Cowboy Bebop, Lupin III, Samurai Champloo, etc.) I think the only anime I watched that was supposed to be a comedy and I loved was Cromartie High. I would like recommendations of shows like that. Or really any good anime. I don't want to watch Bleach, One Piece, Naruto, or FMA (I tried to watch FMA but got bored).
The important note I must make is that I tend not to enjoy a series if it has too many anime cliches or the humor isn't actually funny. I know that's opinion, but maybe it'll help your recommendations. Thanks.

all of these are either comedy anime or good action or drama shows that should make you laugh fairly often

school rumble
school rumble 2
the melancholy of haruhi suzumiya
full metal panic
full metal panic: fumoffu
full metal panic: the second raid although i dont remember there being as many LOL times
kanon (2006 remake) has made me laugh many times
zero no tsukaima
black cat
rune soldier
slayers
excel saga
today in class 5-2
ranma 1/2
golden boy

Trigun comes to mind along with the ones above.

I've seen most of Trigun but you reminded me to finish it. Thanks.
I'll check out the ones up there I haven't seen. It's hard for me to find a series I can really enjoy and see the whole of because I'm very picky with my anime.

Today in Class 5-2 is pretty good for comedy

Battle Programer Shirase is pretty funny

I second the FMP Fumoffu recommendation.

I'd say school rumble is the ideal place to start. Although, Fumoffu is funnier, but it also somewhat requires you to watch the first season beforehand, which isn't a comedy (although does have good humor at times).

Full Metal Panic: Fumoffu and School Rumble and probably the most popular, and are really good. Same with Midori no Hibi.

Excel Saga
Ebichu
Furi Kuri (FLCL)

Really good too but you need to keep an open mind and don't think any dirty thoughts, for once.

Kare Kano (or His and Her Circumstance) >_>

kare kano doesnt end though LOL :(

Perhaps Air-Gear would be good? I liked it.