There already is a thread for this:
Unfortunately I am afraid this thread will sink soon. That is what always happens with this kind of threads. Regardless that...
City Hunter - Action/Comedy. Ryo Saeba is a "sweeper" (a combination of hitman and private eye) that solves crimes in Tokyo. Together with his friend Hideyuki they form the "City Hunter" agency. Ryo is (in)famous for being a true professional, a brilliant detective, an excellent fighter, an unbeatable sharp-shooter... and a real leech that only accepts female clients. Hideyuki dies early on the series and gets replaced by his sister Kaori... who is not in love with Ryo, no, no, no, but she will pummel him if he hits on a client or behaves like a pervert. Needless to say, it happens often. This series is DOWNRIGHT hilarious, with good drama moments to balance the comedy and gorgeous art. All characters are interesting and deeper than they sound like. The manga is better than the anime.
Maison Ikkoku - Romance/Comedy/Drama. Yusaku Godai is a lovable, candid, clueless ronin (student who is trying to pass college entrance exams) that lives at Maison Ikkoku (a run-down boarding house)
with a pack of loons and jerks make his life impossible. One day he has got enough and is walking out the door, bags in hand.... and he walks in Kyoko Otonashi, a beautiful, short-tempered woman who announces herself as the new manager. In order, Godai's suitcase, jaw, and heart hit the floor. Godai starts a "win Kyoko's heart over as passing college over and surviving lunatic neighbours" campaign, but his dificulties increase when he finds out that Kyoko is a widower... This series is an excellent blend of touching drama, comedy and weirdness. Both manga and anime are totally worth to check.
Rurouni Kenshin - Historic/romance/drama. Year 1878. Kaoru Kamiya, heir of a kendo dojo meets Himura Kenshin, a wanderer swordsman (or rurouni) that ten years ago was a legendary assassin during the conflicts of the end of Tokugawa Shogunate. She talks him into staying in his dojo to help her. Kenshin believes he has finally found a place to call home. However, soon he learns the ghosts of the past will not stay buried... Check the manga. It is way better than the anime.
Fist of North Star - Martial arts/drama/post-apocalyptic. In the enar future, nuclear war has turned the world into a barren wasteland. Human civilization has collapsed. In this situation, food and water are the only things worth, and the only law is the law of the jungle. Gangs of thugs and bandits roam the devastated wastes, preying on the weak and helpless with impunity. In this situation, Kenshiro, the titular hero, wanders from town to town, looking for his fiance Yuria kidnapped by his once best friend, as he protects those who can not protect themselves with his lethal martial art, the Fist of North Star, a fighting technique destroys internally the adversary's body. This manga has influenced most fighting mangas since it was published. The artist is excellent, the action is explosive, and -make no mistake about it- this series is VERY emotional.
Kimagure Orange Road - Romance/Comedy. Kyosuke Kasuga is a teenager whose family has moved several times to hid they have psychic powers. Shortly after arriving a new city, he meets Madoka Ayukawa, a beautiful, warm and nice young girl he inmediately likes. However, when he meets her in his school, she acts cold to him, and everyone tell him she is a delinquent he should stay away from. At the same time, Hikaru, Madoka's best friend, gets a crush on him. However Kyosuke has fallen in love with Madoka (in spite of her vonfusing and constant mood shifts) and only sees Hikaru like a friend. Meanwhile, Madoka IS in love with Kyosuke but she would never betray her best friend... and there you have it. This series defined love triangle in anime, and it stands over other romantic comedies due to the charism and depth of their main characters. Watch the anime first, but the manga is worth to read.
Claymore - Medieval fantasy/drama/action. In a medievalesque world plagued by demons, an organization creates the claymores, half-human/half-demon hybrids to fight the demons, named claymores. A claymore called Claire meets a boyd named Ranski and she adopts him after he was cast out from his town. Ranski follows Claire as she goes from deadly fight to deadly fight.
Saint Seiya - Fantasy/action. In a world where pagans gods reincarnate every century to fight using armored human champions, a Japanese child named Seiya gets forced to leave the orphanage where he lived and travel to Greek to become a warrior of Athena -named "saint"-. After undergoing an inhuman training he earns the Pegasus armor and travels back to Japan to get reunited with his sister. Little he knows, this is only the beginning of a series of battles between gods to protect/rule over the planet. This series has a bunch of flaws but they are overweighed by its good parts. And it is my childhood. Watch the anime, disregard the movies, and check the last saga of the manga.
Slam Dunk - Basket/romance. Rowdy, temperamental high school student Hanamichi Sakuragi hates basket after still another girl turned him down in faour of a basket player. However, when he finds Haruko, he decides becoming a basketball plaer in order to win her over. Often he plays matches, though, he finds out that he LIKES bastket. In fact, it is turning him in a better person.
Gundam/Gundam Zeta - Sci-fi/robots. Too long to summarize in a post, but this is one of the best robot anime and one of the most popular and influential anime done, period.
Dirty Pair - Sci-Fi/action/comedy. In the far future, humanity has spread across the galaxy, but that doesn't mean there aren't any problems any more. In fact, there are quite a lot of them, and some of them are worse than people could have dreamed of before going into space. An agency of the galactic government deals with these problems by dispatching teams of highly-trained, well-equipped troubleshooters, called "Trouble Consultants", to solve the trouble. One of the most successful teams of Trouble Consultants is the "Lovely Angels", two teenaged girls who have a near-perfect success record. However, they also have a reputation of blowing up everything they touch... which is unfair. Only a third of their missions end with something being destroyed, and it's never their fault (so what if some of the things they have accidentally blown up are inhabited planets? It was an accident!), which has led to their unofficial and hated nickname of the "Dirty Pair". This anime is a riot and it is highly recomendable.
Edit:
Ranma 1/2 - Martial arts/comedy/romance. Ranma Saotome and Akane Tendo are two young martial artists whose parents have got them engaged to join both fighting schools. Obviously, neither of them is happy about the situation, and they argue constantly. Complicating matters, Ranma is cursed to change sexes when splashed with water thanks to an idiotic training of his idiotic parents. And then a parade of wacky characters, plenty of them wanting marrying or killing one of them comes to town. This manga has action and crazy comedy. It is part of my teen years.
Urusei Yatsura - Sci-fi/romance/comedy. The life of slacker, lecher, dumb teen Ataru Moroboshi changes completely when an alien fleet arrives to Earth to invade it. Though they declare they will leave peacefully if one of them -Ataru- wins the leader's daughter in a tag team game. After ten days Ataru manages winning the game, but his troubles have just begun. The alien girl has fallen in love with him.
Mazinger-Z - Robots/action/drama. During an archeaological expedition to a Greek island, a scientist named Dr. Hell found an army of ancient, humongous mechas beneath a maze of ruins. Deciding using them to take over the world, he kills all remainder scientists in the expedition, but one. Dr. Kabuto manages running away and goes back to Japan, where he devotes several years to build a weapon capable to fight Hell's humongous mecha. Hell gets him assassinated to prevent him from becoming an obstacle, but not before Kabuto handed over to his grandson Kouji his creation: the super robot Mazinger-Z. This series did not create the genre, but it defined it. In case of you do not care for the Monster-of-the-week format the anime follows, the manga is better. And darker. Mazinger-Z has two sequels, Great Mazinger and Grendizer. the latter is maybe the best of the trio.
Record of Lodoss War - Fantasy/drama. In other world, armies of gods battled each other until their mutual annihilation. The two last combatants were Marfa, goddess of creation and Kardis, goddess of destruction. Before dying, Kardis cursed the Earth where she fell, but Marpha split it from the mainland, creating the cursed island of Lodoss. Through the centuries, Lodoss would be the theatre of endless wars between good and evil. Fantastically animated, this anime is a classic of the high fantasy genre.
Lone Wolf and Cub - Seinen/historical/action/drama. This story happens in the eighteenth century. Itto Ogami is Shogun's executor. However, the powerful Jagyu clan covets his position, so they murder his family except for his son Daigoro, and frame him for high treason. Ousted and revengeful, Itto abandons the Code of Samurai and becomes a ronin assassin, wandering Japan together with his son while planning his revenge. This manga is a seinen, so do not expect shonen's normal tropes. It is VERY dramatic and bloody.
Sailor Moon - Shojo manga/magical girl/romance/actino. Usagi Tsukino believed she was an average girl until she met Luna, a talking cat revealed she was a sailor senshi, a magical warrior whose duty was finding and protecting the Moon Princess and defeating Dark Kingdom. However Usagi can not achieve that alone. Classic shojo manga. The manga is superior to the anime in everything but art.
Gatchaman/Battle of the Planets - Sci-fi/action/drama. Earth is threatened by an international terrorist organization of technologically advanced villains, known as Galactor is trying to take control of the Earth's natural resources. To oppose to them is created a team of five young scientifically-engineered ninja super-heroes: the Gatchaman Team. Another classic super-hero anime.
Again, I'll add more recomendations when I have more time.
Edited by Jenskott, 13 May 2014 - 01:13 PM.