Dance in the Vampire Bund: A young man with a glandular problem has to keep a thirteen-year-old royal Tsundere mass murderer safe when she founds a nation for her extended family (of mass murderers). Her three cousins really want to love her.
Deadman Wonderland: A young boy bleeds profusely in a quest for candy at a twisted place that looks happy on the outside. Once he no longer needs the candy, he looks for an albino in the same twisted place.
Death Note: Honors student plots to conquer the world by writing names in a book, uses sex appeal when that fails.
Alternatively: A small but focused police effort is launched to stop a straight A-student from writing in his diary. Eventually the entire world suffers for it.
An ordinary (but brilliant) Japanese boy gains a special power with one specific use and lots of caveats. He uses this power to realize his dream of changing the world for the better... by destroying the old one. He does this with a cryptic-sounding secret identity and incredible planning. Death Note or Code Geass
Digimon Adventure: Children are sucked into the Internet and are assisted by advanced artificial intelligences while coming out of various states of denial.
Digimon Adventure 02: A child genius takes online role-playing way too seriously. Five kids decide to troll him by destroying everything he's built online. They later become friends and team up to fight Anime Tommy Wiseau.
Alternately: Digimon Wonderswan Series: An 11 year old boy is called to fight a ongoing war in a parallel dimension, with a humanoid abomination-slash-cosmic horror, separated from all he knows and loves. This war eventually takes him on a vast journey through space and time, and into alternate universes. Eventually, this horror is transformed into an egg, which the boy takes with him, to never to return to his own universe.
Digimon Adventure: A year before that, 7 children visiting a summer camp, is flung into the same dimension, in order to handle the comparatively minor side-effects of that ongoing war, never learning what exactly is going on, nor their true roles.
Digimon Adventure 02: 3 years later, the 7 children, along with a few others, return to that dimension, in order to handle further problems caused by that war, and unwittingly cure one of it's victims of his infection.
Dogs: Bullets & Carnage: A genetically modified albino, his one-eyed, red-headed cigarette-loving partner, a scarred amnesiac woman with a katana, and a retired assassin... try to figure out what the plot is about.
Doraemon: A time-traveling cat with no ears tries to prevent a loser kid from growing up to be an even bigger loser.
Dororo: A deformed swordsman quests to get his body parts back from his father's former business partners, teaming up with a kleptomaniac juvenile delinquent along the way.
.hack//SIGN: A kid cannot log out from a MMORPG. His friends spend a lot of time discussing the problem.
Legend of the Twilight Bracelet: A boy falls in love with a very young mother and helps her find her kid, who has spent months in the video game.
Bardock - The Father of Goku: Hero's dad foresees his planet and people getting blown up by a camp tyrant.
The History of Trunks: Teen goes back in time to prevent group of heroes from getting killed by killer robots.
Dragon Ball GT: The aforementioned blonde ape gets turned into a nine-year-old kid and has ball-hunting adventures with his own granddaughter, a purple-haired CEO, and a robot. He later turns into a pink ape and fights dragons that don't really look like dragons.
Dragon Ball Kai: The filler-free version about a group of heroes fighting intergalactic evil while getting killed, but they get better.
Dragon Crisis!: Boy gets forcibly dragged by his cousin, in order to help gets this box from the Mafia, which turns out to have a dragon in it. Said dragon falls in love with him.
Duel Masters: An epic saga of card games, wisecracks, and hair.
Eyeshield 21: A coward adopts a secret identity, acquires a horrible nickname, gets repeatedly shot at and visits Las Vegas because his upperclassman thinks they can win the Japanese high school Super Bowl with three guys and a dog.
Or: An eighteen year-old female wizard wants to join a group of wizards who are known for causing large-scale property damage. She succeeds, only to find out that most of the guild are varying shades of crazy
Or: Boy with a lumpy head is molested by his housemaid and a homeless person. Robots ensue.
Or: A young boy's coming of age story where giant robots come out of his head.
A young boy growing up in a small town where nothing interesting happens learns how to play baseball, ride a motorcycle, and use a guitar. He finds that women are hard to understand, is embarrassed by sudden changes in his body, realizes that adults aren't any more mature than kids, and defies authority figures in order to make his own choices.
Getter Robo G: A new fat guy joins the other two and pilots a new mecha to fight demons. He doesn't die.
Getter Robo Go: A new team pilots a new version of the robot that runs on plasma energy. Everyone hates it.
Getter Robo Armageddon: In a Crapsack World, a new team pairs up with the old team using a kickass version of the robot while fighting eldritch abominations. Then, they go and blow up Jupiter.
Shin Getter Robo vs. Neo Getter Robo: The fat guy dies in the beginning so that the team from the hated series becomes cooler. Even the cowboy is cooler. And they still fight dinosaurs.
Ghost Hound: Three middle-school students are drawn into the raging battle between psychology and parapsychology. Freud ensues!
Ghost Hunt: She's a spooky story-loving high school girl! He's a paranormal investigator! Together, they go hunting for spirits!
Ghost in the Shell: A lawbreaking police Canon Sue uses work to surround herself with coworkers that remind her of opposite attributes of her own personality, fight her customers and have sex with a mass murderer and conceive and raise too many children with said mass murderer.
Innocence: Depressed cop and his partner talk about philosophy with everyone they meet. There is also a plot involving dolls.
Gintama: In a world with an alternate history, a group of people who by all means should be fighting for justice instead take on odd jobs to pay their rent.
Or: Sporadically employed veteran with unhealthy eating habits makes his way in post-war Bakumatsu-era Japan. With aliens.
Or: Silver haired samurai, Chinese alien girl and a Straight Man with glasses team up to try and fail to pay their rent, also take turns with an elite samurai police made up of a mayonnaise lover, a sadist and a gorilla to do justice in alien populated Japan. Hilarity Ensues.
Girl Friends: Four schoolgirls discuss nail polish and question their sexuality.
Glass Fleet: The French Revolution is kind of weird in space. Narrator spends most of the series disguised as her dead brother. Primary antagonist loses interest when he finds out she is not her dead brother, for whom he had strong (and somewhat bugnuts-crazy) feelings. Lots of people angst.
Glass Maiden aka Crystal Blaze: A loser turned private eye saves a naked amnesiac glass sculptor, only her old bosses want her back.
Grenadier: Ms. Fanservice with a BottomlessCleavage wanders around, shooting people and persuading them that guns are bad (in that order). The primary antagonist is a clown who floats around killing people with an air-gun.
Guilty Crown: Girl with BroCon wants to mate with brother; said girl causes the Apocalypse.
GunBuster: High school girls learn to pilot a Humongous Mecha, time dilation causes angst, and breasts bounce for the first time ever in anime.
Gungrave the Anime: White-haired young daughter of a deceased mafia boss inherits a 6+ foot tall undead bodyguard armed with big freaking guns who's on a quest for revenge.