Animeleague

Well, I've run into a few of these.

Ultimate Teacher
Basically a man who's part cockroach escapes from a secret laboratory and comes to the school with the worse discipline in Japan, intending to bring to it his own twisted form of order. He just didn't count on her... It's especially weird, but has a lot of fan service in this.

Project A-ko
A-ko is a very unusual and energetic high school girl. You get a hint why she's like that when you finally get a glimpse at her parents at the end. Lot of fan service in this one.

Ranma 1/2
Two training buddies in a dojo make a promise that one day their children will marry and thus join two families together. However, when the prospective groom arrives to meet the man's three daughters, he's carried in over the shoulder of a panda - and is a girl. Things just get stranger after that. Some fan service, mostly it's a martial arts romantic comedy.

Dominion
A young motorcycle cop transfers into the Dominion Tank Police - the group who takes on the worse of criminals in this poluted city. Some violence, fan service.

Mezzo DSA (Danger Service Agency)
A bit like Black Lagoon, an ex-cop, a gaget happy engineer and one serious bad girl with a pair of M1911's is going up against creeps, thugs, and assassins. Definite fan service.

Video Girl Ai
After the girl Yota is interested in confesses to Yota's best friend, only to be rejected, Yota stumbles across a magical video shop that specializes in unrequited love. However, there's something strange about the video tape he rents from this place, as the girl in the video starts climbing out of his television... This predates The Ring, I'm pretty sure it influenced it. Some bad behavior, cursing, and fan service.

Cowboy Bebop
Humanity has spread throught the solar system, in large part due to special gates that allows for rapid transit between colonies. It also means rapid getaways out of police jurisdiction. Cowboys are the new bounty hunters - and they only get paid if they bring back the bounty alive. Of course, nobody said this was going to be easy.

Ghost in the Shell
Section 9 is a special operations force - counterterrorism and cyber crime - all the more important as cyborgs are now a common element in society and someone is going around hacking people's brains. Major Motoko Kusanagi is determined to get to the bottom of this. The events in the later anime series are a prequil to the original movie.

Akira
As rival motorcycle gangs battle on the streets, Tetsuo has a chance encounter with an escape psychic from a classified military facility - and gets brought in as a new psychic. And it's up to his friend Kaneda to rescue him, with help from the same group that tried to liberate the psychic. Because the psychics have had a vision - Akira is returning, and the newly awaken and powerful Tetsuo is intent on meeting him.

Neon Genesis Evangelion
Fifteen years after a small cataclysm, Shinji Ikari is summoned by his father to Tokyo-3 for a very important job - to pilot a giant Evangelion against the angels, who are immune to conventional and nuclear weapons. However, there's a lot of secrets in this city, including what the Angels are after and what the people who possess it will do. The end is very gory.

Hellsing, Hell Girl, and Claymore should appeal. Something a bit more modern you may also enjoy is The Promised Neverland (The orphanage is not what it seems). I also enjoyed Black Butler (Victorian - the young lord of a wealthy family makes a deal with a demon, to find out who killed his parents) and Bleach (A young psychic finds himself in a secret war between Soul Reapers and the Hollows).

You may also enjoy Dead Mount Death Play - a necromancer gets reincarnated in modern Tokyo - inside the body of a boy who's just been killed. And the assassin can't understand why he's still alive...

I don't know if you can get hold of these anywhere.

Mnemosyne: Mnemosyne no Musume-tachi
Rin: Daughters of Mnemosyne

Immortality is something many people would wish for. But would it be such a coveted ability if people knew they would be subject to countless attacks because of it? Such is the case for Rin Asougi, an immortal private investigator, because there is no shortage of people who want her dead. Over the centuries, she has met many grisly ends, but each time, she returns to life as if nothing had happened.

In 1990, while looking for a lost cat, Rin runs into Kouki Maeno, a man who feels that his memories are wrong. Agreeing to help him, Rin discovers that Kouki is not what he seems, all the while drawing closer to her true enemy. This adversary knows Rin and her kind all too well, and if she dies by his hand, she may stay dead permanently.

Elfen Lied

Lucy is a special breed of human referred to as "Diclonius," born with a short pair of horns and invisible telekinetic hands that lands her as a victim of inhumane scientific experimentation by the government. However, once circumstances present her an opportunity to escape, Lucy, corrupted by the confinement and torture, unleashes a torrent of bloodshed as she escapes her captors.

During her breakout, she receives a crippling head injury that leaves her with a split personality: someone with the mentality of a harmless child possessing limited speech capacity. In this state of instability, she stumbles upon two college students, Kouta and his cousin Yuka, who unknowingly take an injured fugitive into their care, unaware of her murderous tendencies. This act of kindness will change their lives, as they soon find themselves dragged into the shadowy world of government secrecy and conspiracy.

Kashimashi: Girl Meets Girl

Hazumu was a shy boy who enjoyed gardening, collecting herbs, and long walks in the mountains. One day he finally worked up the courage to confess his love to Yasuna, but she rejected him.

Depressed, he wandered up Mt. Kashimayama, the place where they first met, to reconsider his feelings. After getting lost, he wished upon a shooting star and received a bizarre twist of fate.

Now he is a she, and she stumbles headfirst back into social life and relationships only to find that the entire landscape has changed!

Kiss x Sis (TV)

After Keita Suminoe's mother passed away, his father promptly remarried, introducing two step-sisters into Keita's life: twins Ako and Riko. But since their fateful first encounter, a surge of incestuous love for their younger brother overcame the girls, beginning a lifelong feud for his heart.

Now at the end of his middle school career, Keita studies fervently to be able to attend Ako and Riko's high school. While doing so however, he must resolve his conflicting feelings for his siblings and either reject or succumb to his sisters' intimate advances. Fortunately—or perhaps unfortunately for Keita—his sisters aren't the only women lusting after him, and there's no telling when the allure of temptation will get the better of the boy as well.