A genre of manga and anime that's targeted towards college-age boys (mid-teens to mid-twenties). Literally means "young man," or "adult age," and is pronounced "say'-nin."
Seinen is also popular with girls of that age, though not as popular as it is with the target demographic. It usually involves an 18-20 year old male lead getting caught up in a love triangle (or square, or pentagon, or just with someone who can't stand the sight of him). Almost always has a happy ending, though some of the best ones are the ones that end in tragedy.
Examples of seinen works: Maison Ikkoku (the godparent of the genre), Video Girl Ai, Aa! Megamisama, Everyday Is Sunday, and the more recent Love Hina. To a milder extent, even Neon Genesis Evangelion and Gundam have seinen side-plots (the Shinji vs. Asuka/Misato/Rei bits of Eva). Ikkoku and Love Hina both have the five-way unrequited love angle, while Ai and Aa! Megamisama both take on a more "forbidden love" angle (the main love interests aren't quite human).
In most anime magazines (like Newtype), seinen shows are glorified beyond their actual popularity - the recent Love Hina has been featured in the last four issues of Newtype with posters, booklets, and huge feature articles. And L.H.'s ratings aren't/weren't all that good. My guess as to why is because most of the male staff writers at Newtype (and other magazines) are just growing out of their seinen stage and don't want to want to let go yet.
Seinen often contains some ecchi elements, but they generally occur in the first few episodes/chapters (to draw their audience in). Quite often, they aren't even in the story, but in the marketing (advertisements, posters, fan works, and other such goodies). More often than not, seinen tries to draw boys away from the more raunchy hentai out there, and almost never involves anything sexual beyond kissing and typical male daydreaming.
Another aspect of seinen works is the raw emotion found in it. Seinen authors pride themselves on making boys cry, and without making fun of their physiology, it requires using a lot of realistic and sometimes harsh situations in the stories. Getting dumped, getting put on the spot in the worst ways, and even death is used to wreck the reader's assumedly tough heart. Granted, most seinen aren't quite that heartbreaking, especially once they're watered down into anime (the manga is better than the anime, always).
Though the genre is relatively new (early 1980's), seinen stories are often remembered in the same way one would remember a first girlfriend, sort of. Not the most socially advantageous when out on the dating scene, but the stories stick and the female love interest becomes the epitome of the "perfect woman" - see also all the Belldandy worshipping going on around here. Most guys who are affected by seinen in that way tend to preach about it's greatness to younger guys in hopes of getting them hooked on their silly dreams of some chaotic but perfect relationship (sort of like a cult or the freemasons, now that I think about it...). See also the above paragraph about Newtype and my ulterior motives for creating this write-up.
Seinen, of course, is also the best form of visual entertainment ever known to mankind. The $1000 plus shipping for the Maison Ikkoku DVD box set (all 96 episodes and 2 movies) was well worth saving for.
See also: Shounen, Shoujo