Action/Fighting
ClaymoreStory: The world is festering with monsters called Youma, who disguise themselves as humans and eat living guts. The only people with the ability to slay these monsters are Claymores, women who are half-Youma themselves. Claymore follows the story of Clare, an especially unique Claymore with her own agenda
Length: 26 episodes
Fullmetal Alchemist: Brotherhood
Story: Two brothers, Edward and Alphonse Elric, use a forbidden alchemic ritual to bring their departed mother back to life, but it fails, leaving Edward without an arm and a leg, and his brother a soul trapped in a suit of armour. Together they quest to find the Philosopher's Stone, a relic which is said to make any alchemic endeavour possible, and on the way discover a deeper plot
Length: 51 episodes
Kenichi: the Mightiest Disciple
Story: After years of being picked on by bullies, pipsqueak Kenichi decides to learn self-defence at Ryozanpaku dojo; but the dojo has some of the craziest masters he has ever met, and his troubles only seem to get worse as his training intensifies!
Chrono Crusade
Story: A Nun named Rosette has a bond with a demon named Chronos, together they battle the forces of Evil in the world, but Chrono is hiding a dark secret...
Length: 24 episodes
High School of the Dead
Story: The Zombie Apocalypse has broken out! The terror forces an unlikely group of highschool students to bond together and try to survive; full of great, well-rounded characters and amazing action sequences
Length: 12 episodes
Sword of a Stranger (movie)
Story: A young boy on the run from some foreigners who want to use him as a sacrifice enlists the help of a masterless samurai.
High School/Slice of Life
Angel Beats!
Story: Otonashi wakes up in a strange high-school setting, and finds himeslf recruited by a group called the Afterlife War Front, fighting against a strange girl called Angel. But as the fight goes on, Otonashi finds there is more to this world than it seems
Warning, this anime WILL make you cry
Length: 13 episodes
Arakawa Under the Bridge
Story: Kou Ichinomiya has always lived obsessively by one creed: Never be in debt to anyone! But when a strange girl called Nino saves his life, she declares the only way to pay her back is to love her, and he quickly discovers this will mean living with her and her strange compatriots under the bridge!
Length: 13 Episodes
Ouran High School Host Club
Story: Haruhi, a middle-class, serious student, gets into the fancy Ouran Academy on a scholarship, and soon is kidnapped by the extravagant Host Club! A group headed by "King" Tamaki, their club practices entertaining ladies and fulfilling every ladies desire to be loved, but there is one thing no one must ever discover... Haruhi is a girl!
Length: 13 episodes
Black Rock Shooter
Story: Kind of hard to describe, and differs whether you read the books, watch the OVA, or one of the TV series;
http://en.wikipedia.org/wiki/Black_Rock_Shooter
Length: ??
Taishou Baseball Girls/ Taishou Yakyuu Musume
Story: In the Taishou era of Japan, when just as many girls wear Kimonos to school as Sailor Uniforms, one girl desperate to prove her competence and independance despite being female, forms the very first all-girl baseball team! This story focuses far more on the lives of the girls and their personal stories more than the actual game, so I don't class it as a sports anime at all.
Length: 12 episodes
Chobits
Story: Penniless and technologically illiterate cram school student Hideki Motosuwa finds an advanced artificial life form called a Persocom in the trash! Taking her home, he manages to boot her up, but finds she can only say "Chii". He names her Chii and lives with her day to day, unaware of her mysterious past. This anime also raises some strangely serious questions of what it means to be human, and what it means to love.
Length: 27 episodes
My little sister can't be this cute!
Story: Also called "Ore no Imōto ga Konna ni Kawaii Wake ga Nai" and often shortened to Oreimo, this anime focuses on Kyosuke, a normal high-school student who is always being held second to his 'perfect' little sister, who is popular, gets good grades, likes modelling and normal girl activities... and is secretly really into Anime and games; especially ones with a 'little sister big brother' romance theme! When he stumbles into her secret, he becomes heavily involved in hiding her secret life, and helping her accept her true self
Length: 12 episodes
Horror
Elfen Lied (18+ for nudity and gore)
Story: Lucy, a powerful creature called a Diclonius, has gotten loose from the lab where she was kept as an experiment; her survival depends upon destroying all of human kind, but her personality splits between the ruthless and secretive Lucy, and the innocent and childlike Nyu, who is taken in by two innocent bystanders.
Length: 13 episodes
Higurashi When They Cry (18+ for gore)
Story: Based on a visual murder mystery novel about a mysterious village and untimely deaths; I reccomend reading the wiki article first or the anime will be confusing
Length: 26 episodes
Future Diary/Mirai NikkiStory: Yukiteru Amano, a junior high student, has trouble making friends. He views himself as a spectator from the sidelines and often writes down what he sees in a cell phone diary. Tormented by solitude, Yukiteru interacts with his imaginary friends Deus Ex Machina, the God of Time and Space, and Muru Muru, Deus's servant. One day, Deus grants Yukiteru's cell phone the ability to record the future for the next 90 days. Yukiteru is then forced to participate in a battle royale with eleven other people, each of whom also have a diary that can predict the future in some unique way. The rules of the game are simple: before the world ends on day 90, the contestants must find and kill all the other contestants, and the last one standing will become Deus's successor.
Length: 26 episodes
I'll add more as I think of them!