I'd need to hear a high amount of praise, from people whose opinions generally concur with mine, for these titles to leave this section.

Not really my sort of thing Comment
Ai Yori Aoshi (TV) Too much fanservice.
Black Lagoon (TV) Sounds too action-oriented.
Burst Angel (TV) Sounds too comedic.
Ceres, Celestial Legend (TV) Too much of a fantasy element.
Claymore (TV) As above.
Code Geass: Lelouch of the Rebellion (TV) Mecha without any romance.
Cowboy Bebop (TV) Bang.
Divergence Eve (TV) Sounds too comedic.
Eat-Man (TV) Strange concept
El Hazard - The Magnificent World (OAV) Sounds too comedic.
Ergo Proxy (TV) Sounds too scary.
Fantastic Children (TV) Too much of a fantasy element.
Full Moon o Sagashite (TV) Shoujo.
Fullmetal Alchemist (TV) Too much of a fantasy element.
Gakuen Alice (TV) Magical Girls.
Gantz (TV) Sounds too scary.
Genshiken (TV) Sounds too uneventful.
Ghost in the Shell: Stand Alone Complex (TV) I don't like multiple canons.
Grave of the Fireflies (movie) Made by the same person who made Pom Poko.
Gungrave (TV) Sounds too action-oriented.
Honey and Clover (TV) Sounds too uneventful.
Honey and Clover II (TV) As above.
Kaleido Star (TV) Gymnastics theme.
Karas (OAV) Too much of a fantasy element.
Kiddy Grade (TV) Sounds uninspired.
Kino's Journey (TV) The motorcycle can talk.
Love Hina (TV) Harem.
Madlax (TV) Girls with guns.
Mushi-Shi (TV) Too much of a fantasy element.
My-HiME (TV) As above.
NANA (TV) Shoujo.
Nodame Cantabile (TV) Musical theme.
Noir (TV) Girls with guns.
Paradise Kiss (TV) Fashion theme.
Patlabor The Mobile Police (OAV 1/1988) Sounds too comedic.
Perfect Blue (movie) Sounds too scary.
Popotan (TV) Harem.
Revolutionary Girl Utena (TV) Shoujo.
Rurouni Kenshin: Trust & Betrayal (OAV) Samurai.
Sakura Wars (OAV) Sounds uninspired.
Shakugan no Shana (TV) Too much of a fantasy element.
Simoun (TV) Yuri. Gender switching. Religious theme.
(The) Slayers (TV) Sounds too comedic.
Sword of the Stranger (movie) Samurai.
Tenchi Muyo! (OAV 1/1992) Sounds too comedic.
Texhnolyze (TV) Sounds too scary.
(The) Third: The Girl with the Blue Eye (TV) Sounds too action-oriented.
Tokyo Godfathers (movie) Strange concept.
Trigun (TV) Sounds too action-oriented.
(The) Twelve Kingdoms (TV) Too much of a fantasy element.
Utawarerumono (TV) As above.
(The) Vision of Escaflowne (TV) As above.
Welcome to the NHK (TV) Sounds too comedic.
Whisper of the Heart (movie) It's romance, but also Miyazaki.
Witch Hunter Robin (TV) Too much of a fantasy element.