My taste in pretty much any sort of media tends to be very eclectic, and this applies to anime as much as anything else. While I can appreciate most genres, I have a particular fondness for weird, random humor shows like Excel Saga and Pani Poni Dash.
With that in mind, would somebody care to supplement my meager knowledge of japanimation and make a few recommendations along those lines?
FLCL
Minami-ke
Sayonara Zetsubou Sensei
Sayonara Zetsubou Sensei is by SHAFT, same animation studio that did PPD. It’s somewhat on the same vein, except much more relaxed, thematic and doesn’t rely on a billion impossibly obscure anime references and background text for its jokes (Those there are some of those anyway). I actually liked it a lot, even though PPD bored me to death. Also, you’ll be hearing the two opening themes in your head until the day you die.
Seto no Hanayome is a much more straightforward show: Guy gets rescued by mermaid, mermaid is forced to marry him, parent of the mermaid are Yakuza and the father wants to kill the guy, the setting abruptly changes to school setting and hijinks ensue. Despite the overdone to hell premise, it just happens that it’s actually awesome. The setting is old, but the cast is amazing and it just gets funnier the more it goes. The Terminator is involved. And it had one of the most FUCK YEAH-worthy endings ever.
I second that Minami-ke (plus its sequel, Minami-ke Okawari) and also add Lucky Star
I have seen SZS. It took a few episodes to grow on me but I thoroughly enjoyed it once it did. Rumba rumba rumba rumba rumba…
I tried Lucky Star, but that I couldn’t get into.
I’m fond of Gintama. It’s not in the same vein of Excel Saga or PPD or Lucky Star. It’s not wacky like that, but it IS a comedy and occasionally parodies popular shonen fighting series.
It’s almost spiritually similar to Ranma, in that there IS a plot in the background that only comes to the surface periodically before being swept away for more one-shot episodes, and also the fact that the anime frequently follows the manga chapters out of order, but the structure of the series allows for that to flow well. Also, miraculously, the anime-only filler episodes aren’t terrible, a lot of em are actually quite good.
Currently about 71 episodes subbed and it’s still going. For some reason or another no one has licensed it for North American release yet, I can’t really understand why. It’s not a series for everyone but I imagine it WOULD fit nicely on Cartoon Network. Ah well. It means you can easily find it still on Animesuki.
Here’s a couple of series you may like.
School Rumble’s a good choice if you like ridiculous love triangles (and love rectangles, and love pentagons, and love stately tetrahedrons, an so forth…).
Ramen Fighter Miku (or however it’s called) is another wacky (albeit short) series about attempted ramen delivery, fighting, and rather wacky characters (so my synopsis sucks I probably would’ve done better if I could’ve found a Wikipedia article on it).
Two other shows that I also recommend even though their plots keep them from being silly all the time (they at least have some really silly episodes).
Denou Coil isn’t a humorous series for the sake of being a humorous series (in fact some episodes are somewhat depressing), but some of the filler episodes are downright hilarious in their awesomeness (hell I recommend watching it regardless of how silly it is just out of the sheer amount of awesome that show is).
Tower of Druaga: tAoU’s short but it’s got some priceless episodes as well (actually the whole damn thing is free off of youtube among other places).
Ouran High School Host Club repeatedly made me laugh so hard I cried. It’s not completely random, but most of the episodes are pretty self-contained although there’s an overarching plot of sorts.
Bobobo-Bo Bo-Bobo.
I mean, I don’t like it, but it’s silly anime.
Oh yeah, you might also like Genshiken
Magical Shopping Arcade Abenobashi if you like dipping into different genres of weird, from RPGs with insta-death random encounters to detective stories where getting killed equals getting chibi’d.
Oh, no you didn’t go there!
Abenobashi gets too serious by the ending (it’s pretty existentialist) but I agree that the early episodes are a riot. 
If you want my personal opinion… The following list shows the best anime i’ve ever seen.
One piece. The main character is extraordinarily dumb but strong, and he recruits a group of pirates comprised of all different kinds of people, from a half-man half-reindeer to a money obesessed navigator. It has a serious storyline and plot, with a bunch of fighting, but i think it’s worth it.
Full Metal Alchemist. Funny? No. Awesome? Yes. About a boy who uses alchemy to get his brother and himself back to their original bodies after losing a leg and an arm of his own and his brothers entire body during an alchemy accident.
Trigun. Funny? Yup. Awesome? Absolutely. Trigun is about a man who’s lived hundreds of years because he’s actually a Power Plant, who doesn’t want to kill anyone h=and has a brother who wants to annihilate the entire human race. Hijinks ensue.
Uhhh… That’s actually all. Those three anime series are really awesome. there are 300 something one piece episdoes, and about 50 trigun and FMA episodes. Have fun.
Trigun was funny for the first eight or nine episodes, then devolved into super-serious depressing space opera. I generally found FMA funnier than Trigun when it tried.
Sadly that’s true. Also too bad there were so little episodes. (compared to something like One Piece or Naruto)
Shounen series generally have way more episodes than any other kind of show, because the episodes are mainly rehashes of “me fight this guy! Then me fight that guy!”. Comparing any anime show to Naruto, Bleach, Pokemon et al is just unfair. 8p
While I don’t consider One Piece to be a full comedy, it does contain many How Dumb Was That?? moments that make me laugh. Plus it’s full of likable characters and action. Tony Tony Chopper’s origin story in particular is both hilarious and tragic and the same time. Recommended.
I second Wil’s recommendation of One Piece. Personally I find it to be an example of how to do a Shonen Fighting series right. There’s little to no emphasis on ‘POWAR LEVEL’ (some might argue that a Pirate’s Bounty is a measure of their overall strength and while that is kind of true, a Bounty just reflects the Pirate’s threat to the World Government. After all, poor Chopper is still stuck with a 50 Beli bounty) and despite having gone on for over 500 chapters, the series has still not gotten stale and repetitive.
The creator of One Piece is surprisingly imaginative and creative, and while the series does delve into a certain level of silliness, it never gets completely ridiculous. Everything that happens makes sense within the context of its own world (Even if that world was intentionally made malleable enough so that Oda could feasibly create any scenario he can think of). You just have to keep in mind that real-world physics don’t apply to the Grand Line.
There’s some moments of genuine drama in One Piece (Chopper’s backstory, Vivi’s plea to her people to stop the war, everything that happened at Water 7 and Enies Lobby), but those moments never overwhelm things and the series is essentially still really light hearted and fun. While the series has its low points (Skypeia, and to a lesser extent, 75% of Thriller Bark) it is, overall, very well written.
If you’ve never seen it before and don’t mind catching up on over 500 chapters of manga, and nearly 400 episodes, (and neither are showing any signs of stopping) then look into it.
My only main criticism is that, lately, the anime has fallen back on shortcuts to stretch out the manga content so that they only use about one chapter’s worth of material per episode. Meaning there’s lots of flashbacks to prior episodes at the start of each, and throughout there are even more flashbacks and other forms of repetition to fill up the full 23 minutes. Not terrible, and it can be bypassed by fastforwarding, but it’s still a tad annoying.
Jungle wa Itsumo Hale Nochi Guu. Known as Hare + Guu in the US, but isn’t the original so much more fun to say? Most reviews use the word “neurotic” for Hale, but “frenetic” works better. Guu’s the real star of course. A sadly under-appreciated series from 2002 or 2003, what with the damn kids nowadays having their Minami-kes and their Pixy Sticks and their Rock-em Sock-em Robots.
I can’t really describe Jungle much except that the comedy is as frenetic as Excel’s but avoids the retarded mental disjunction of so many of the series that tried to ape it. Yes, it has lots of jokes thrown at anime and games, but the humor comes from the interaction between Hale and Guu, not from “OOOOOOOHHHHHHHHHHHHHHH THEY JUST REFERENCED STARBLAZERS HAHAHAHA.”
Ah, and don’t let the opening animation scare you away.