This is a whole list of anime for anyone to check out and reference. Post here if you want anything added to the list. If you want any anime recommended I can add something to the list depending on what you're looking for. This is a short list for now but more will be added and you can also add more.
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Death Note - About a boy who gets a notebook which can kill by just writing their name in it. He then uses this power to eliminate all the criminals and becoming god of the new world.
[Drama,Crime]

Bleach - A man who is given the power of a shinigami and uses it to defeat creatures known as hollows
[Action,Drama]

Soul Eater - There is a school for meisters and weapons to train to defeat keishans.
[Comedy,Action,Horror]

Code Geass - A boy has been given the power of geass to control people, he uses this to defeat the Britannian empire and free Japan.
[Action,Drama]

Full Metal Alchemist - A boy in attempts to bring back his mother loses his leg and then gives up his arm to save his brother. Now he is in search of the philosophers stone to get his brothers body back.
[Action,Comedy,Drama]

One Piece - A boy named Luffy who admires pirates that rule the seas mistakenly eats a devil fruit and turns into a rubber man.
[Action,Adventure]

Hikaru No Go - A 6th grader finds an old go board in his attic and discovers a ghost who has an interesting past along with the go board.
[Adventure, Drama]

Wolf's Rain - The wolf Tsume (Claw), hiding his true form, lives as a human. Hanging out in the city, and leading a band of young delinquents
[Adventure,Supernatural]

Naruto - This story follows a boy named Uzumaki Naruto who attends The Ninja Academy
[Action,Adventure]

Higurashi When they cry - After moving into the quiet town of Hinamizawa, Maebara Keiichi spends his days blissfully in school often playing games with his local friends. However, appearances can be deceiving
[Horror,Drama]

Sword Art Online - In the future people can now create virtual avatars of themselves for an online VRMMORPG
[Action,Adventure,Comedy]

Attack On Titan - The last reminiscence of humanity is now forced to live behind walls and fight monstrous giants known as titans
[Drama,Action,Horror]

Go Lion - Go Lion begins in the year 1999, when the planet Altea is subdued and enslaved by the Galra Empire.
[Action,Adventure]

Dead Mans Wonderland - After being framed for the genocide of his class he is put in a special prison where they play a game of life or death.
[Horror,Action]

Magical Warfare - An ordinary boy with a dark past comes across a girl collapsed in a schoolyard in an odd uniform. Since then his life changes forever.
[Action,Fantasy]

World Conquest Zveda Plot - World conquest has something everyone has thought of but never achieved. Until one little girl by the name of Kate Hoshimiya came along.
[Action,Adventure,Fantasy]

Reborn - Tsuna is a failure at everything in school. But that all changes when he meets a baby named Reborn who claims to be an Italian hitman from the Vongola Family
[Comedy,Drama]
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User added animes

Welcome to the NHK - A college drop-out who becomes a shut in (referred to as a hikikomori in Japanese) thinks there is a group known as NHK working against him that made him the way he is.
[Comedy, Drama]

Prince of tennis - A 12 year old boy named Ryoma Echizen who joins the tennis club where he beats other regulars and 2nd years to become a regular on the team. Ryoma continues to progress in tennis hoping to beat one man.
[Comedy,Sports action, Adventure]

Berserk -A man named Guts who is part of a mercenary group called The Band Of The Hawk lead by Griffith. In the beginning Guts had no dream and only felt comfortable with a sword in hand. Watch as Guts gains his dream and as Griffith spirals into a pit of no return.

Persona 4 - Based of the popular game persona 4, the anime follows the life of a boy named Yu narukami who just moved to a town called inaba and he lives with his uncle, Dojima. Murders Start happening in inaba and the police have no idea what is happening.
[Action, Comedy, Crime, Fantasy]

Inazuma Eleven - A group of friends have a soccer team and now are trying to win the FFI and beat all other schools
[Sports, Action]

Inuyasha - This anime is about a demon dog named Inuyasha who fights in a feudal area time. In that time is full of greedy evil demons, who wants a special stone called The Shikon Jewel.
[Action, Adventure]

Blue Seed- Fujimiya Momiji is a descendant of the Kushinada clan whose women possess the power to defeat the Aragami, an alien plant-like race, by sacrifice. After centuries of slumber, the Aragami have awakened and are invading Tokyo en route to conquering the world.
[Action,Comedy,Horror]

Clannad - Okazaki Tomoya is a delinquent who finds life dull and believes he'll never amount to anything. Along with his friend Sunohara, he skips school and plans to waste his high school days away.
[Comedy,Drama,Romance]

Seitokai Yakuindomo - Tsuda Takatoshi enters a school called Ousai Academy, a school that only very recently became gender-integrated. The majority of his classmates are girls, and he encounters various problems and hilarious situations along his way.
[Comedy, School]

Steins;Gate - Steins;Gate is about a group of friends who have customized their microwave into a device that can send text messages to the past. As they perform different experiments, an organization named SERN, who has been doing their own research on time travel, tracks them down and now the characters have to find a way to avoid being captured by them.
[Thriller, Sci-Fi, Comedy]

Elfen Lied - Lucy, a young and psychotic Diclonius, manages to break free of her confines and brutally murders most of the guards in the laboratory where she is being held, only to be shot in the head as she makes her escape. She survives, falling off a cliff into the ocean and manages to drift along to a beach where two teenagers, Kouta and Yuka, discover her. Having lost her memories, she was named after the only thing that she can now say, "Nyuu," and the two allow her to stay at Kouta's home. However, it appears that the psychotic side of Lucy is not dead just yet.
[Action, Drama, Horror]

Darker Than Black: Kuro no Keiyakusha - In Tokyo, an impenetrable field known as "Hell's Gate" appeared ten years ago. At the same time, psychics who wield paranormal powers at the cost of their conscience also emerged. Hei is one of the most powerful of these psychic agents, and along with his blind associate, Yin, works for one of the many rival agencies vying to unlock the mysteries of Hell's Gate.
[Action, Mystery, Sci-fi]

Welcome to the NHK - A college drop-out who becomes a shut in (referred to as a hikikomori in Japanese) thinks there is a group known as NHK working against him that made him the way he is.
[Comedy, Drama]

Persona 4 the animation: Based of the popular game persona 4, the anime follows the life of a boy named Yu narukami who just moved to a town called inaba and he lives with his uncle, Dojima. Murders Start happening in inaba and the police have no idea what is happening.
Yu and his newly met friends with the help of their personas have to stop the murders before any more happen.
[Action, Comedy, Crime, Fantasy]

Sorry if the descriptions suck, i made them off the top of my head

Blubcreator : i will add Clannad:a high school anime very emotional *spoiler alert*don't get attached to the characters some of them die in the after story

rosario+vampire:another high school about a kid who accidently goes to school filled with monsters in human form but humans are forbiddon so he has to keep it a secret

Heh...this has become a spoiler thread rather than reference...

Maybe we should use spoiler tags or make the descriptions with a bit less spoilers.

I wanna add Inazuma Eleven to this list, some may think its stupid but after the first 20 episodes it gets really fun and exciting, It's about a group of friends that try to win the FFI

This thread is a really good idea, if the list gets long enough it'll make a great reference for anyone looking for a new anime. Now, I think popular and well known animes that haven't been added yet, such as Dragon Ball Z and Fairy Tail, should be added just to get them out of the way. It's easy to spot these types of anime and it'll be easy to add them to the list. Plus, they're popular for a reason, so they make great recommendations.

Golden_Zekrom : Omg....another Inazuma Eleven fan! ^-^

I would say animes such as....

Sailor moon- A girl who transforms into a magical superhero girl to fight off evil.

Inuyasha- This anime is about a demon dog named inuyasha who fights in a feudal area time. In that time is full of greedy evil demons, who wants a special stone called The Shikon Jewel. And also theres a girl who accompany him called Kagome.

Blue Seed- I don't think anyone knows much about this anime. It came out before inuyasha so in a way inuyasha is similar to it. Its about evil monsters who goes after the a girl who is a kushinada princess. Well she gets protected by a prince in a sort of way, but not like any normal prince that you would meet.

Kamikaze Kaito Jeanne- This one is also under the category of magical girl. Its about a girl thief who transforms in the night, to steal paintings. But theres more to it than you think.

Special A - now this anime you have got to see...if you need a really comedy anime. This may be the one you want to watch. Its a high school anime. All of the characters have long legs. And theres a rival between a girl and a boy. But really you should watch to find out more.

Flame Of Recca. This anime is packed with action and with magical powers of the sort.

Cardcaptors - This is also another magical girl anime. Its about a girl who finds a special book containing magical cards.

Teknoman- This anime is a mehca-tec, its about a certain guy who uses an special teck armor to fight off evil in space and more.

Flint the time detective- This anime is about a young boy who travels with a boy and girl. To collect special fossils, that contain cute fuzzy looking creatures.

Azumanga Daioh- This anime is based on a school life around 5 young kids. The comedy of this anime, is out of this world. The first episode will get you going. You will be laughing for non stop.

I could say more but I will leave there. I recommend you watch them in English and Japanese. I am old school that's why I didn't add new ones. I would had added DBZ but, someone already has. I hope this helps anyone, for what they want to watch. ^-^

I'll just add a few:

Seitokai Yakuindomo - Tsuda Takatoshi enters a school called Ousai Academy, a school that only very recently became gender-integrated. The majority of his classmates are girls, and he encounters various problems and hilarious situations along his way. [Comedy, School]

Steins;Gate - Steins;Gate is about a group of friends who have customized their microwave into a device that can send text messages to the past. As they perform different experiments, an organization named SERN, who has been doing their own research on time travel, tracks them down and now the characters have to find a way to avoid being captured by them. [Thriller, Sci-Fi, Comedy]

Elfen Lied - Lucy, a young and psychotic Diclonius, manages to break free of her confines and brutally murders most of the guards in the laboratory where she is being held, only to be shot in the head as she makes her escape. She survives, falling off a cliff into the ocean and manages to drift along to a beach where two teenagers, Kouta and Yuka, discover her. Having lost her memories, she was named after the only thing that she can now say, "Nyuu," and the two allow her to stay at Kouta's home. However, it appears that the psychotic side of Lucy is not dead just yet. [Action, Drama, Horror]

Darker Than Black: Kuro no Keiyakusha - In Tokyo, an impenetrable field known as "Hell's Gate" appeared ten years ago. At the same time, psychics who wield paranormal powers at the cost of their conscience also emerged. Hei is one of the most powerful of these psychic agents, and along with his blind associate, Yin, works for one of the many rival agencies vying to unlock the mysteries of Hell's Gate. [Action, Mystery, Sci-fi]

Most of the descriptions came from MyAnimeList because I am pretty bad at describing anime.

Momo, Girl God of Death - (Drama, Fantasy,Supernatural, Psychological) A girl wrapped in white, her name is Momo...in her hand lies a blunt yet shiny scythe. By her side is a wingged black cat by the name of Daniel. Carrying the souls of humans, the girl's existence parallels to that of a "Death God" or "Shinigami". At the instant when this white Death God touches the hearts of humans, the world is filled with kindness and grief... (From MAL)

Panty and Stocking with Garterbelt - (Action, Comedy, Ecchi,Parody, Supernatural) Panty and Stocking—the Anarchy Sisters—are two nasty angels who got booted from the pearly gates for being foul-mouthed b****es! Now they spend their nights blowing up ghosts in the seedy abyss between Heaven and Earth. Panty likes sex, Stocking likes sweets, their afro-sporting main man Garter Belt has a fetish we can't mention. Together, they're turning the mean streets of Daten City into a buffet of bodily fluids. Ghosts don't stand a chance against their lingerie of mass destruction, and if this debaucherous duo can collect enough Heaven Coins, they just might get their halos back. It's a slim chance in hell, but anything can happen when you're rolling commando, especially with Panty and Stocking! (wouldn't recommend for a younger crowd)

Maria†Holic - (Comedy, Parody, School) It’s not easy to find the perfect girl, even when you’re the same sex! Kanako thought attending an all-girls school would be the perfect way to meet the girl of her dreams, but after her hot new roommate turns out to be a guy in drag, and catching the eye of the most popular girl in school only brings down the wrath of all the OTHER similarly obsessed girls, she’s not so sure! Complicate things with a cat-eared dorm leader, her roommate’s rude-mannered maid, an identical twin sister (who attends an all-boys school of course) and WAY too many attractive girls of questionable persuasions and the question becomes whether Kanako will die from frustrated nosebleeds! (Life would be SO much easier if guys didn’t literally give her the hives!) Will Kanako ever find a non-polar opposite of a compatible non-opposing polarity? Let’s just say that the quest for true love will not run straight in Maria Holic.


Unbreakable Machine-Doll - (Action, Ecchi, Fantasy,School, Seinen) Akabane Raishin is now attending the Royal Academy to become the best in the world. Accompanied by the lovely teenage girl Yaya, who is actually Raishin’s puppet weapon, he plans on rocketing to the top of the class. However, his test scores come nearly dead last although his combat skills and determination are second to none. Raishin has to compete with the deadliest of classmates if he wants to come out as the king.(from MAL)

Initial D - (Cars, Seinen) High school student Takumi Fujiwara works as a gas station attendant during the day and a delivery boy for his father's tofu shop during late nights. Little does he know that his precise driving skills and his father's modified Toyota Sprinter AE86 Trueno make him the best amateur road racer on Mt. Akina's highway. Because of this, racing groups from all over the Gunma prefecture issue challenges to Takumi to see if he really has what it takes to be a road legend.

Excel Saga - (Comedy, Parody, Sci-Fi,Shounen) Hyperactive Excel does anything and everything to try to please her lord, Ilpalazzo, who wants to take over the planet. Excel's misadventures takes her and her partner, the ever-dying Hyatt, all over the world, meeting several strange people as they go. Everything is bizarre and goofy, as any kind of anime or entertainment genre gets mocked and spoofed.
 
El Cazador de la Bruja - (Adventure, Mystery, Drama) Ellis, a young girl suspected of murdering a prominent physicist Heinrich Schneider, is on the run from an underground society called "Hunters" when she is tracked down by the bounty hunter Nadie in a small Mexican town. However, instead of turning her in, Nadie impulsively decides to help her and the two girls embark on a journey to Ellis' hometown, where they plan on finding clues about her past. From there, they travel south to search for the mysterious Gemstone of the Inca Rose, the "Eternal City" of Wiñay Marka, and Ellis' own obscure destiny