Anime and Manga are two different storytelling media. They both originate in Japan, and are closely related, but are ultimately two different things. The confusion between the two arises mostly because it's often the case that the same story will have both an anime and a manga version. The terminology will vary a little bit depending on whether the person ...
Elfen Lied (2004)?
I watched that a couple years ago, and it does have similarities, a pink-haired young woman escaping a facility, being taken in by a pair of cousins. She's got powers and doesn't mind turning people into chunks of goo.
Better summary, from MyAnimeList:
Lucy is a special breed of human referred to as "Diclonius," born with a short pair ...
That sounds very much like Nils Holgersson.
It has the tiny boy on a goose.
It is mostly in rural settings.
The drawing style resembles the Heidi cartoons.
I don't know about the old man and the reflection. I've never watched Nils. I see commercials for it sometimes on TV here in Germany.
Picture from Wikipedia:
You are probably thinking of Fate/stay night (or its prequel, Fate/Zero), with a number of details misremembered.
The character who you think is Joan of Arc is actually a genderswapped King Arthur (but until her identity is revealed, people commonly guess that she's Joan of Arc). As such, it is she who uses Excalibur, not her opponents. She is typically ...
Kiki's Delivery Service is a coming-of-age story. The changes reflect Kiki gaining maturity and independance. According to the Nausicaa.net FAQ:
Jiji doesn't speak (in human words, at least) to Kiki anymore, because
they grew up, not because she lost a power. In the original book, it
is explained that a witch girl and a black cat are raised together
This is Onegai! Samia-don, (AKA Please! Psammea-don, AKA おねがい!サミアどん)
A Japanese anime
that was broadcast from 2 April 1985 to 4 February 1986 with a total
of 78 episodes produced. This anime is based on the 1902 novel Five
Children and It by English author Edith Nesbit.
The anime differs from the novel in revolving around four children
Aero Troopers (2003)?
From the jacket below, which features a robotic-looking fish (and what do you know, it's got Mark Hamill in it!):
In a world beyond imagination where fantastic tree villages float in mid air, a young boy named Joshua dreams of adventure. Forced from his home by an evil mechanical beast called Nemeclous, he discovers a fantastic ...
The characters depicted in the picture are blue-eyed Yato (holding the sword) and red-eyed Yukine in the reflection in the sword, two of the tri-tagonists from the anime series Noragami.
The image itself is an original work by fan-artist Haru titled 唯一無ニ ("the only one")
Definitely Huntik (2009-2012).
According to Wikipedia,
In India, the series' first season aired on Disney XD (India) in 2010.
There's Lok, the blonde guy who discovered his father's amulet. While studying with a friend (Sophie, the skirt girl on the left), it is revealed that his father, who was missing, may be alive. Lok and his friend go on a quest ...
This sounds like Elfen Lied. The pink haired girl escapes from a holding facility and brutally slaughters all guards standing in her way with her powers. Their deaths are very gory indeed. During her escape she is shot and falls into the sea. She is later found on a beach by a boy and a girl that takes care of her.
I believe this is Deltora Quest
The evil Shadow Lord has taken control of the kingdom of Deltora and has driven the land and its people into misfortune and suffering. Lief, the son of a blacksmith, has just turned sixteen and is entrusted, along with his two companions Bard and Jasmine, with an important mission: to retrieve the stolen seven magical ...
No, Goku is not unbeatable. As a matter of fact, it is one of the running themes of the Dragonball Series that Goku is often defeated, is either forced to retreat or killed, and while retreating or "dead" trains his abilities up to new levels. The rest of the Z-fighters often have to hold the fort while he trains.
Son Goku's power level varies widely across ...
This is the end of 'The End of Evangelion' where we see the results of the "third impact". In short, crosses appear everywhere, then various other weird stuff happens and keeps happening until the entire audience is completely baffled. Then it starts to get downright obtuse.
Actually (of course this is just coming from personal experience) it's an Asian cultural idea that food is a very important part of life. If you really do some research about say, Chinese culture you will notice how much more important and precious food/eating is to them compared to Western people. This is why in Japanese anime, Korean manga, or whatever it ...
This character is Armonia Justin Beyondormason, one of several shinigami from the anime and manga series Death Note. While a few shinigami are major characters in the series, interfering in the world of humans, Armonia only appears in a handful of scenes taking place in the shinigami's own world.
His golden, jeweled appearance in the anime is based ...
Sounds similar to Samurai Champloo episode 11 "Gamblers and Gallantry".
"Jin comes to the rescue of a lady in distress. He falls in love and
tries to rescue this woman from the hard life she has come to face.
Will he save her and himself? In the meantime, Mugen trains a
rhinoceros beetle for a bug-fighting tournament in which he expects ...
Most Shōnen shows, at least, are probably following Dragon Ball Z
Dragon Ball Z was the starting point for a great deal of the anime that followed it. Many of the best-known anime draw heavily from Dragon Ball Z, by direct admission of the creators.
One Piece was so inspired, according to Wikipedia.
Naruto was also probably influenced by Dragon Ball Z:
This sounds like it's Techno Police 21C, originally released in 1982.
Some matching details:
the main character, Ken, is a motorcycle highway cop. at the beginning of the movie, he is called to join the police force in Centinel City after getting into trouble for wrecking yet another motorcycle.
he has a robot partner named Blader, who is blue and white ...
There was no one better suited for the job than the 3rd Hokage, Hiruzen Sarutobi, after his successor, Minato Namikaze was killed trying to re-seal the 9 Tailed Fox demon, Kurama, within his son Naruto.
The 3rd Hokage was considered one of the most powerful shinobi to have ever lived and carried among his list of titles, God of Shinobi (忍の神, Shinobi no Kami)...
In Castle in the Sky (1986) there is an ancient, broken robot that is later reanimated and begins attacking people.
The young boy (Pazu) doesn't find the robot, but he and a young girl (Sheeta) are taken to a fortress where the robot is already being studied. The "bad guys" were attempting to repair it.
There is a scene later in the movie where Pazu and ...
This is a distorted remembering of Hayao Miyazaki's Princess Mononoke produced by Studio Ghibli.
The young man is Prince Ashitaka.
The young woman, is San, daughter of the wolf goddess Moro, often called by the sobriquet "Princess Mononoke".
The "women of the forge" are a group of former prostitutes who work the giant bellows in the main forge in Iron ...
I have found the anime I was looking for. It’s called Monsuno.
The show revolves around "re-awakened Monster DNA called Monsuno" that finds its way into the unsuspecting hands of adventure-seeking teenagers Chase, Jinja, and Bren. Accompanied by their Monsuno, Liger, Charger, and Quickforce, they are searching for Chase's father Jeredy Suno, the creator ...
This is Magic Knight Rayearth (1994-1995) as found by Steve-O in the comments and confirmed by the OP. It is also an adaptation of a manga series of the same name by Clamp that from 1993 to 1996.
Hikaru Shidou, Umi Ryuuzaki, and Fuu Hououji are strangers brought together by fate when they meet during a seemingly normal field trip to Tokyo Tower. ...
It's when reality hits you like a brick to the face.
Their goal was to convert the AI to side with the humans, by showing it a better reality where the machines (the bug that created the tendrils) were the "bad guys", while also showing the positive aspects of humanity - sex, games, excitement... And then the humans rescued the AI from the tendrils, ...
Sounds like Saber Rider and the Star Sheriffs. From Wikipedia:
The series is set in the distant future. Humans have spread beyond Earth and colonized planets across the universe, creating a New Frontier of man. In order to protect these new settlers and maintain laws and regulations in the New Frontier, Earth's Cavalry Command was created. Cavalry Command ...