I’ll start with the ones other people already described.
Claymore - Started off pretty generic, but it’s getting better.
El Cazador de la Bruja - Not really good, but not bad enough to give up on.
Tengen Toppa Gurren Lagann - Seraphim’s picture doesn’t do the show enough justice. Kamina is the greatest anime character ever. And Simon evolves from obnoxious whiny coward to awesomeness.
Bokurano - 14 high schoolers and 1 little sister must pilot a giant robot to protect the earth. Oh, and piloting it uses up their life force, so they die immediately after the battle. The series is more about the personal lives of the kids (one has no regard for the lives of others, one’s messing around with her teacher, one blames his little sister for their mother’s death, and so on) than the monster battles.
Darker than Black - Some catastrophic event occurred ten years ago and now there are people with super powers called contractors. The details of how the contractors obtain and use their powers is a mystery linked to a structure called Hell’s Gate (or was it Heaven’s Gate? One of which blew up and destroyed South America).
Ergo Proxy - A girl in a dystopian future searches for the truth about the world, and there are these monsters called proxies that, umm, I’m not sure what their purpose is.
Hayate no Gotoku - A poor high school-aged boy is left an enormous debt by his parents and ends up working as a butler for a spoiled rich girl. There is much randomness, humor, and references to other anime and video games.
Kanon (2006) - Harem anime based on an H-game. I think Yuichi is channeling Kyon from Haruhi.
Murder Princess - A princess and a katana-wielding (female) bounty hunter accidently swap bodies. The princess offers herself as a reward if the bounty hunter will save her kingdom. Ass-kicking and lesbian-undertones ensue.
Nagasarete Airantou - A boy gets washed up on an island that lost all of it’s male population 12 years ago. Guess what happens next. Fortunately, after the second episode, the girls stop acting so rabid and there’s more focus on the absurd nature of the island.
Romeo x Juliet - Has very little resemblence to the Shakespearian play. I wouldn’t be terribly surprised if they survived the series. At least it looks pretty.
Seirei no Moribito - Middle-aged female spear-wielding bodyguard must protect a prince possessed by a water-spirit. The emperor needs to kill the prince because the water-spirit will cause a catastrophic drought.
Seto no Hanayome - Because he has seen a mermaid, boy must marry her to not be killed. The mermaid’s family are yukaza. Episode 10 is funny because of Terminator-like character and references.
The Skullman - A masked vigilante is taking revenge on corrupt officials who were involved in his father’s death. I think. The main character is a journalist who is investigating the unusual incidents.
Sisters of Wellber - A lady thief and a princess must deliver a message to a semi-distant kingdom to prevent war. The thief is also searching for some sinister figure from her past. Very slow fansub releases.
Sola - Feels kind of like Kanon with less harem. A boy with an obsession for taking photos of the sky meets a strange girl. Girl is actually a vampire-like creature (weak to sunlight, no blood-drinking). The girl knows his sister.
Shaman King - Fairly standard shounen action show with a laid-back lead character.
Le Portrait de Petit Cossette - Gothic love story. Boy falls in love with ghost of murdered girl, must atone for killer’s sins be being painfully tortured by the spirits of the inanimate objects that saw the murder. Trippy art style.
School Rumble and School Rumble 2nd - More love triangles and mistaken confessions than you can shake a stick at.
Will start watching soon:
Kurau - Phantom Memory