I've watched a couple dozen or so anime, and about the only two I could stand were Akira and Ghost in the Shell. I'm not sure why, but I note the lack of cutesey neon-haired bimbos with dinner-plate-sized eyes in either of them, that could be crucial.
Any recommendations along those lines?
Ergo Proxy might be interesting for you. Another slightly far-fetched guess would be Witch Hunter Robin. Just a hunch, I might be wrong. xD
I've watched a couple dozen or so anime, and about the only two I could stand were Akira and Ghost in the Shell. I'm not sure why, but I note the lack of cutesey neon-haired bimbos with dinner-plate-sized eyes in either of them, that could be crucial.
Any recommendations along those lines?
Death Note. All non-anime-watchers and not-as-hardcore-fans like it.
That's not cute! I watched Elfen Lied you know!

Elfen Lied has soul; very much so in fact. Higurashi is just sick

I'm gonna be diplomatic and say they all rock!
As people here actually seem to have watched quite a lot of anime, I'm gonna try to recommend some less famous ones. =D Almost all of these are "serious" anime.
Kimi ga Nozomu Eien: If you liked Higurashi, you'll like this one. Practically zero gore though.
Chaos Head: HOLY SHIT THEY'RE AFTER ME-anime. It's pretty f*cked up, but I don't remember how bad the anime was. I'm currently reading the manga in Japanese.
Denpa Teki na Kanojo: A short 2x40min anime series about a guy stumbling over psycho girl after psycho girl. Higurashi-fan recommended.
Innocent Venus: Not the best one, but nice and not too long. Maybe a little too cute for Sproingie, but it doesn't really "use" it (it's not ecchii). Pretty short anyway.
Mai Hime: Surprisingly powerful. Pretty slow in the beginning, but halfway things start spiraling downwards.
Kaiji: Disturbing. Guy gets indebted and is forced to participate in completely insane game shows hosted by rich bastards. Again, I found it disturbing in a negative way. >_>
Serial Experiments Lain: A "Wait, what?" anime. It's weird, but I think it's pretty deep.
Planetes: A serious space anime. No warp engines, no VTOL Tintin rockets, just a pretty physically accurate space anime. It's awesome in more ways than that though.
Shadow Star Narutaru: Pretty old anime. Basically cute girls with Pokémons fight... uh... someone.
The Sky Crawlers: The Crysis of anime. The 3D dogfight scenes are extremely well done. The anime character style is a little different though. The story is awesome too!
EDIT: And Shuffle!.