I don’t know why I’m defining this, since anyone who’s interested in the topic already knows what it is, but “bishounen” means “beautiful boy” in Japanese, and refers to a particular type of young man much to be seen in animé. “Bi-” specifically refers to feminine beauty, and bishounen are often beautiful in an androgynous kind of way. Shoujo (girl) animé is rife with them. (Some Western otaku refer to any handsome man as a bishounen, but I regard this as a weakening of the term.)
Anyway, mine include the following:
Amiboshi from Fushigi Yuugi;
Miki Kaoru from Revolutionary Girl Utena (although I understand it becomes more bishie-intensive - and more hentai - after the first season, which is all I’ve seen to date);
Issei from Please Save My Earth;
Pretty much all of them from Ceres (Yu Watase may be homophobic, but she draws a damn fine bishie);
Trowa and Quatre from Gundam Wing, whom I’ve just spent quite some time reading fanfic about;
and of course, I’d be remiss if I didn’t mention Skids and Harley from Sandra Delete’s magnificent Boy Meets Boy.
So who’s yours?
So, no biseinen? A real loss right there. It’s also making this list a thousand times harder.
Anyway, my favorites right now are:
Subaru Sumeragi from CLAMP’s Tokyo Babylon & X. The older Subaru is better-looking, but I’m not sure if you could include him as a bishounen.
Touya, Yukito, & Yue from Card Captor Sakura
Ran from CLAMP’s Clover
I’ll just go ahead and say all guys from CLAMP’s works. They’re really all the same person anyway.
Duo from Gundam Wing (yumm…fanfic…)
Hisoka from Yami no Matsuei
jessica
Wotthehell, let’s be generous and fling the door open to biseinin too. 
(Anyway, half of these people look five years older than they’re supposed to be. Hotohori from FY is 18? WTF?
The most egregious example, of course, though not a bishie, is Lady Une from GW. She’s supposed to be 19! That girl ain’t seen 19 in a long time.
Is this, like, the Japanese answer to the Star Trek Irregularly Aging Infants problem, wherein Naomi Wildman suddenly shows up looking like she’s 10, 6 years after she’s born?
But I digress. Back to bishies. My roommate reminds me of Squall from Final Fantasy 8.
I should say, he just mentioned Squall to me. My roommate isn’t actually an aloof, scarfaced mercenary.
Woohoo!!! Biseinen make me happy. Shounen-ai just feels weird if the relationship looks like it’s between two 11 year old boys.
Half of them may look five years older, but that’s balanced by the fact that the other half look five years younger. Hisoka from Yami no Matsuei is 16. He looks like he’s 12.
But, onto biseinen:
Masa, Enjouji, and Ranmaru from Kizuna
Zechs & Treize from GW
All the guys from Yami no Matsuei
Other random characters I’ve come across and can’t remember at the moment.
Very fun. My friends and I talk about this all the time. They’re hooked on Yu Watase’s stuff, so they’re a bit partial to characters from Fushigi Yuugi. My tastes are CLAMP.
jessica
First of all:
I KISS YOU! I agree. Particularly egregious is referring to anyone from DBZ (save Trunks, Zarbon, or Android 17) as a Bishie. (And even Trunks is borderline. Favours his father a little much.)
You’ve already mentioned my favourite: Quatre Rebarba Winner, Gundam Wing (honourable mentions go to Duo and Zechs as well). However, I detest Trowa, and though it’s inescapable, I really, really don’t like the idea of 3X4. 2X4, on the other hand… 0:)
Kuja and Zidane, FFIX.
Ferio, from Magic Knight Rayearth (and Clef from the OAV version).
Several guys from Weiss Kruz, though I’ve only seen art, so that, unlike any of my other choices thus far, is strictly for looks. 0:)
Erk…mind blanks at the moment…will probably post more later.
Wait…last minute entry which I almost forgot for some bizarre reason…Marron Glace, of Sorcerer Hunters.
Damn auto-smilies…Insert 0:) above where appropriate.
Sephiroth(FF7)
Zack(FF7)
Bel Cain (Elemental Gearbolt)
Ialu(Elemental Gearbolt)
Citan Uzuki(Xenogears)
ID(Xenogears)
Delita(FFT)
Ramza(FFT)
Nephlite(Sailor Moon)
That’s about all I can think of for now.
Oooh… I second Subaru Sumeragi, my favorite anime character ever.
Dee and Ryu in Fake were also pretty cool.
What was the name of the archaeologist with glasses from Tokyo Babylon? I liked him too.
Archaeologist? I don’t think there was one…the closest character I can think of is Seishirou Sakurazukamori, Subaru’s boyfriend/tormenter/whatever you want to call it. He was a veterinarian.
Of course, it’s been a while since I read the manga, so I could be forgetting someone.
jessica
No, not the evil dude. The other guy. Was he a historian? Dammit. Um, well, when Hamish gets home I’ll ask him. Argh.
He dug up old buildings, and looks like Seichiiro (not Seishiro) from X.
I could track down a friend who’s really big on X and ask her, if you’re desperate to know. 
Because I really can’t think of the guy.
Ah, well.
My roommate Moishe just started watching Fushigi Yuugi again. It may be homophobic but at least it had Amiboshi/Suboshi together. Rowr!