-Uzumaki: Awesomely disturbing horror manga about.. well, a spiral. Very Lovecraftian. Lots of body horror and eldritch abominations. Junji Ito is the best. Especially since his style is mostly realistic, which makes the really ugly stuff even more unpleasant.
-Hayate x Blade: Comedy/action about a girls' school with bokken fights (it's not kendo, as there aren't that many rules). Somewhat yuri-ish, has some good fights and characters.
-Princess Resurrection: Weird supernatural comedy/action. Basically it's about a guy who gets smacked with a truck and is resurrected to serve a princess (shock!) as an undead (and fairly hard to kill) blood knight. Overall it's very fun and contains references to just about every classic movie monster ever, as well as some good old-fashioned violence. Also notable for having Hime, who is awesome.
-Aria (the first two volumes are called "Aqua"): Just a very calm, relaxing story about gondoliers on Mars. That's most of the story right there, it's best when read slowly, taking in each gorgeous scenery shot and reflecting on the significance of what the characters are doing. Interestingly, there is actually some philosophy in here too.
-Strawberry Marshmallow: Yeah, this title doesn't do it any favors. Still, it's a really funny and wry comedy. One of very few comics that have actually made me laugh out loud when reading it.
-Kashimashi: Okay, so the plot is a little crowded with silliness. There are aliens in this, and they wear spandex for basically no reason whatsoever. Nevertheless, it's a surprisingly moving story about a (possibly transgendered) boy who accidentally gets killed (by the aforementioned aliens) and also accidentally brought back to life as a girl. The result is a love triangle between her and her two closest friends. One of very few Yuri mangas to be (legally) translated for us, so it's definitely worth it if you have any interest in the genre at all. Bizarrely, the manga has a completely different ending from the anime (it's a love triangle, you can probably figure out what this means).
-Blame!: Long, dark story about a person going through an endless, bleak mechanical city. There's practically no dialogue in this, but the art carries the story really well.
-Iono-sama: They only ever translated one volume of this, but it's a sweet and funny Yuri manga about the queen of an unnamed European country traveling the world gathering, um, consorts. It's written by Fujieda Miyabi, so it's much fluffier and happier than that description makes it sound.
-Moyashimon: Agriculture. More engaging than you'd think.
-Fuan no Tane:A collection of short and really, really short horror stories. Some of them are creepy, some are not, some are just goofy. Definitely worth reading for the creepy ones though.
-Gyo: Another Junji Ito manga. This time about zombie fish with robot legs. Really. Not as good as Uzumaki, but worth it for the awesomeness of a fucking shark breaking into a house. Not an anthropomorphic shark, an actual photorealistic shark with robot legs. For real. Also worth it for the fucked up Enigma at Amigara Fault bonus story (unrelated to the story).
-Mushishi: Guy can see invisible creatures in ancient Japan, travels and helps people.
-Tomie: Yes, another Junji Ito manga. I rate it higher than Gyo but not as high as Uzumaki, but it's definitely one of his better works. The plot can be summarized as "immortal demon girl kills and eats people and reproduces by being dismembered".
-Ame-iro Kouchakan Kandan: Miyabi Fujieda yuri manga. At this point you're either going to read it or avoid it.
-K-ON!: Fuck yes.
-Amanchu!: By Kozue Amano, author of Aria. Diving. Relaxing.
-Shoujo Sect: Calm, relaxing y-Hah! Got you, it's porn this time.
-Sasameki Koto: God, I really do recommend a lot of yuri, don't I. I really like the protagonist of this one though. No matter who you are, you'll relate to her. Coincidentally, she looks a bit like the main character of
-Aoi Hana: Like a less silly and frivolous version of the above (or vice versa with the other thing vice versa'd as well). Yuri. People living and having relationships. Incredibly beautiful for a romance manga.
-Miyuki-chan in Wonderland: I've read this two or three times and I'm still not completely sure what the hell it is. CLAMP does erotic fantasy, I guess.
-Sunshine Sketch: Ume Aoki. Moe in wideface.
-Azumanga Daioh: Has anyone not read this or seen the anime?
-Yotsuba: By the author of Azumanga Daioh, but softer. Reaches Calvin & Hobbes levels of awesomeness sometimes.
-Let's play with Kaoru-kun!: I may just be fucking with you at this point.
-Boogiepop Phantom: Actually, don't read this. The anime is better.
-Giant enemy crab: Attack its weak point for massive damage.
-Death Note: I am just fucking with you at this point.
EDIT: I should probably have read your preferences more thoroughly. Still, I don't think my recommendations significantly offend them. However, does "no Shoujo/Romance" mean [no romance and no shoujo] or [no romance that is also shoujo]?