Hajime No Ippo: A young man gets famous for getting hit in the face alot.
Hana-Kimi: A girl cross-dresses and enters an all-boys boarding school on the other side of the world in order to hang out with a guy she's seen on TV but never met. She doesn't do a very good job of keeping her gender a secret, accidentally makes another boy think he's gay, and somehow ends up sleeping in the same bed as said idol an improbable number of times. UST ensues.
Hands Off!: Pretty boy moves in with Grandfather and seemingly germaphobe cousin. Finds out he has psychic powers. Uke and cousin, along with boisterous friend, become impromptu detectives. Labeled as comedic drama. Should be labeled incestuousboy-love.
Happiness: A show about magical schoolgirls, where the most popular character is a trap.
Hols: Prince of the Sun: A boy and his pet bear get roped into killing the devil. Meanwhile, a girl who said boy acts kindly to, tries to turn his whole village against him several times. They're still friends at the end.
Hunter × Hunter: Boy passes the world's most grueling license exam, then uses a fishing pole to fight an evil clown, a band of shady mercenaries, and other maniacs.
Or maybe this: Two boys take an exam; one flunks it and the other barely passes. Then, they go beat up some handicapped people, hang out with gangsters, play an ultra-violent video game, and stomp on an ant colony.
Jewelpet (first season): A magical rabbit arrives late at an important event and that makes her a chosen hero. She has to room with a loser, catch potentially lethal tiny creatures who have jewels for eyes and save humans from becoming stoned by a chibi Maine Coon cat.
Jewelpet Twinkle: In this often misspellt anime, the same magical rabbit needs to find a girl that'll attend school with her. Her immediate choice is another loser. They spend their time growing balls for a high-competition school tournament and stopping a literally raging crossdresser from reading a book.
Or: Every country in the world is going straight to Hell. An androgynous motorcyclist pretends not to notice.
Kirby of the Stars: A baby soldier from space hangs out with a pair of kids and eatseverything in a world where almost nobody has legs. A knight goes behind the back of the king to teach the space-baby how to properly be a copycat. Meanwhile, said king orders a new Monster of the Week from a company he continually fails to realize belongs to the embodiment of all evil.
Or: A penguin(?) and a snail buy dangerous products to kill a baby. They fail every time.
Koe de Oshigoto!: A 16-year old high-school girl is forced by her older sister to do voice acting for an adult game company. She finds herself enjoying it and even displays a knack for it. No, it is not a porno.
Koi Kaze: A guy in his mid-twenties who still lives with his dad goes on a date with a girl 12 years younger than him. Gradually they fall in love. They're siblings.
K-On!: Schoolgirls stay after school to practice their music, but instead eat cake and talk.
Kotoura-san: A little girl is abandoned by her friends, her parents divorce and dump her on her creepy grandfather, and her cat dies. She gives up on other people and lives a dull, depressed life for years. Romantic Comedy!
Kurenai: A poor high school boy takes care of a seven-year-old girl whose goal is to learn to fall in love. Make the mistake of calling this a Lolicon show, and you will bring the wrath of its fans down upon your head.
Kyouran Kazoku Nikki: A family consisting of a supernatural cop, a catgirl, a little girl, a lion, a biological weapon, a gay man and a jellyfish attempt to teach each other the love of family to not destroy the world.
Or: Teenage Japanese boy falls through a toilet into another world. He thinks he's in a classic medieval shonen series, but what no one's telling him is that he's really a magical girl.
Kyoshiro to Towa no Sora: A Japanese teenager with an increasingly messed-up family tries to murder three expies and a blonde girl (each of whom can summon magic mecha) because he thinks that's what his dead brother probably wanted. The blonde one falls in love with him and helps him in his quest. He falls in love with one of the expys. His brother wasn't dead and he gives up eventually.