According to Scott McCloud in Understanding Comics, the very medium of comics, which most people assume began with Rodolphe Töpffer in the mid-1800s. Instead, Scott McCloud includes everything from comic books to Egyptian tomb paintings, making the medium Older Than Dirt. However, he does this by using a broad definition that is far from being universally accepted.
The cover of Uncanny X-Men #136 (Cyclops holding Phoenix) may have been inspired by an older work of art, but it is sufficiently different from Michelangelo's Pietās to be considered in a different category from them. (For starters, Cyclops is standing, not sitting). And the Pietā representation of Mary and Jesus had itself been used by plenty of sculptors for 150 years before Michelangelo was even born, to say nothing of not dissimilar artistic representations of other mothers with dead children dating back to pre-Christian times (e. g. Eos and her son Memnon, Niobe and one of her daughters).
Wizard magazine, the most "mainstream" magazine on comic books, once contemptuously referred to the immortal supervillain Vandal Savage as "a cheap Ra's al Ghul knockoff". Actually, Vandal Savage predates Ra's by 28 years — 1943 and 1971, specifically.
The year before Vandal Savage appeared, America's Greatest Comics had Bulletman fighting the Man of the Ages, a man who had been causing evil for a million years.
Ming the Merciless (1934) has been referred to as "a cheap Ra's al Ghul clone" as well. Ra's and Ming are knockoffs of Fu Manchu, who wasn't the first Yellow Peril villain either.
It's a meme among Fantastic Four fandom that Trelane from the Star Trek: The Original Series episode "The Squire of Gothos" was ripped off from FF villain Infant Terrible, apparently for no more reason than being child-like and omnipotent, even though there are hundreds of examples of this combination going back at least to the 1920s.
Many people seem to think that Aquaman came before Namor the Sub-Mariner, even though Namor predated him by two years. This may be because Namor went out of print during The Interregnum, while Aquaman held on as an Action Comics backup.
The DC Comics skull-faced supervillain Doctor Destiny is often called a knockoff of Skeletor, despite the fact that he predates him by several decades. Besides appearance and the fact that they're both villains, these two characters have absolutely nothing in common. And a skull face is not exactly a new or unique concept to start with.
a man "of iron" with skin so tough that it can withstand anything short of an exploding artillery shell;
able to jump so high it's like he's flying;
imbued with a high morality and sense of justice;
who hides his true ability from everyone;
fights a wrestler for money;
singlehandedly builds a fortress in a wilderness;
has adventures where he lifts a car, and rips the door off a bank vault...
The character is Hugo Danner, Gladiator, from a book published in 1930, before Superman or Spider-Man. Siegel & Schuster have admitted to taking inspiration from it when they created Superman.
Even better, Marvel later created a character named Gladiator as a Captain Ersatz of Superman for their own universe, bringing it full circle. Read more about that here: 
DC, which published a few stories of the original Hugo Danner (as did Marvel), gave Danner a son named "Iron" Munroe who filled in for Golden Age Superman in the Retcon patchwork that The DCU's World War II history became Post-Crisis, when many of the formerly Golden Age heroes were given new, recent origins. Now, the adventures that happened to Superman During the War, mostly happened to Munroe instead.
A number of comic book fans commented that the spaceship◊ in the European comic book Valerian was plagiarized from the Millennium Falcon. Except Valerian and his ship were created in 1967, and Star Wars was made in 1977.
Others commented that the flying cars seen in one of the Valerian stories were plagiarized on The Fifth Element — forgetting that the idea of flying cars has been around since... well, the invention of the car. The story was published years before the movie was made, and the director is a Valerian fan who specifically asked the series' artist to work on the design of the movie.
Some have claimed Watchmen's ending, in which the world unites against an alien threat after New York City is destroyed, is an attempt to capitalize on post-9/11 feelings. However, not only does Watchmen predate 9/11 by 15 years, but the eerie similarities between 9/11 and Watchmen's climax have been noted by more than a few people, especially in regards to whether Ozymandias' plan to bring about world peace would work even temporarily in real life given that world sympathy for the United States was temporary and only lasted until the United States invaded Iraq.
An in-universe example has Superboy saying to Superman "Second star to the right and fly till morning." When Superman says "Peter Pan. How appropriate." Superboy replies "What are you talking about? Captain Kirk said that." in reference to Kirk's closing line at the end of Star Trek VI where he was clearly quoting Peter Pan.
In fact, Word of God has it that virtually all of the characters Moore created for Watchmen were originally to have been Charlton Comics superheroes that DC had recently purchased the rights to; when he couldn't get permission to use them (i.e. the Question), he created pastiche versions.
Many fans of misfit superhero teams who are hated and feared by the public they protect and are led by charismatic wheelchair-bound men often think that DC's Doom Patrol is a blatant ripoff of Marvel's more popular X-Men. Other comics fans who know a little more about the books' histories know Doom Patrol was actually published first, and assume the theft went the other way around. In fact X-Men followed Doom Patrol by only three months, and given the lead time involved in the production of comics it's most likely no plagiarism was involved. However, some artists and writers worked clandestinely for both companies, and it is possible that information flowed one way or the other.
Well, when one property's Rogues Gallery is The Brotherhood of Evil and the other's The Brotherhood of Evil Mutants, it's pretty obvious SOMEONE was reusing ideas.
Except that both Brotherhoods debuted at the exact same time. Both showed up in March of 1964. Yep. Same month of the same year. Making it pretty damn hard for either to be a rip-off.
Stan Lee spoke at the promotion of his "add a caption to a photo" book in 2009. In it, he specifically said that he created the X-Men because his publisher (maybe wrong title) wanted something to compete with Doom Patrol. (Lee wanted to call the book "The Mutants," but his boss over-ruled him.)
Lee himself has admitted that he has a poor memory, so it is possible that he is misremembering. It is all but impossible for the X-Men to have been inspired by Doom Patrol, as it usually took over six months to develop a comic in the 60's. As mentioned above, there were three months between the two teams' respective debuts, which would mean that the X-Men would have already been in the works when Doom Patrol hit the stands.
Adamantium is most famous as the fictional metal Wolverine's bones and claws are made of, and indeed the X-Men movies are credited with bringing the term to the general public. What fewer people know is that adamantium actually predates the creation of Wolverine by several years, as it was first introduced in an issue of The Avengers back in the 60's as the material Ultron's body was made of.
On the subject of the X-Men, the concept of superpowered mutants predates them even at Marvel. The second issue of Yellow Claw from 1956 features six mutants with psychic abilities who are manipulated into using their powers to help the Claw's evil schemes.
Jimmy Woo: Yes, I said mutants, chief! People with deviations...in either mind or body...or both!
On a more general focus there had been superpowered mutants even earlier in science-fiction novels, notably Stanley G. Weinbaum's Adaptive Ultimate (Astounding Stories, November 1935, adapted into the movie She Devil in 1957). And Wilmar H. Shiras wrote a series of pulp stories about superpowered mutants persecuted by a world that fears and hates them starting in 1948 under the general title Children of the Atom.
The mix of ancient characters with original creations in stories about characters like Marvel's Thor and Hercules and DC's Wonder Woman leads to an understandable amount of both Older Than They Think and Newer Than They Think. Notable examples include reviewers thinking a character was being antisemitic for calling Hercules's wife "Hebe" (that's her name, from classical Greek mythology).
Brian Azzarello's wildly popular Batman story Joker, about (you guessed it) The Joker, takes place in a more realistic universe, where the Joker is depicted as a more believable psychopath. His long messy hair, splotchy "makeup", and Glasgow Grin made him a very unique version of the character.... until The Dark Knight came out. Many people consequently thought that the comic "ripped off" Heath Ledger's Joker, or that the story was set in the Christopher Nolanmovieverse. However, this was just a coincidence, they had already started the story before they even saw what Ledger looked like.
The comparison is only appearance based however, as Ledger's Joker and Azzarello's Joker have very different personalities. And the plot of the Graphic Novel was inspired by the 1989 Christopher Walken movie King Of New York.
We first went to the moon in 1969. Snoopy was there earlier that year. Tintin predates Snoopy by 16 years, going to the moon in 1953. Donald Duck already went there in 1948. But Jules Verne's Around The Moon predates everyone (nope—see below), being published in 1870. That's 99 years before Real Life. In From The Earth To The Moon nobody set foot on the moon.
James A. Owen received a lot of hate mail for "stealing" the characters of Titania and Oberon from Neil Gaiman's Sandman series for his own Starchild series. It got so bad that, as a favor, Neil wrote the intro for the collected anthology explaining that James did not, in fact steal anything that wasn't already stolen.
Some fans have accused Spider-Man Arch-EnemyNorman Osborn (aka the Green Goblin) of being a rip off of Lex Luthor, because both are Corrupt Corporate Executives. Thing is, Norman's been an evil businessman since he debuted in 1966 (his Goblin alter ego debuted two years before he did interestingly enough), while Luthor was a traditional Mad Scientist from his appearance in 1940 until his reinvention as a businessman in 1986.
Masked crimefighter who is actually a blind man whose work includes court trials. You are probably thinking about Daredevil, who is actually Matt Murdock, a blind lawyer. But years before him, in 1939, there was another character like that: blind DA Tony Quinn AKA The Black Bat.
Alpha Flight was launched by great fanfare with a major selling feature being it was the first major superhero title featuring Canadian characters. In fact, Captain Canuck had been running for a number of years by that point, and the Alpha Flight character Guardian bore more than a passing cosmetic resemblance to the Captain (Guardian was introduced in 1978, but Captain Canuck had debuted in 1975).
Batman ripped off Dick Tracy characters a lot, if not necessarily intentionally. (Dick Tracy predates Batman by almost a decade.) A guy with his mouth frozen open in a huge grin? That wasn't the Joker originally, that was Laffy, who had many of the Joker's personality traits to boot. (Laffy met a tragic end when he starved to death after his jaw was inadvertently wired shut in an effort to fix his face.) And whom do you picture when you're asked to imagine a guy with a comically long nose? The Penguin, right? Well, he was preceded by another Tracy villain, Ribs Mocca, who looked just like the Penguin except for being much skinnier.
"Broadway" Bates, a Tracy villain introduced in 1932 not only has a long nose, but formal dress, a monocle and a cigarette holder. The current Dick Tracy writers have lampshaded this by claiming "Broadway" has a brother called Oswald in an unnamed city known for costumed heroes...
A villain whose modus operandi is leaving riddles. Sounds like the Riddler? Actually before that was Doctor Riddle, a hunchbacked Bulletman villain who first appeared in 1942, while the Riddler first appeared in 1948.
The superhero's arch-enemy, a bald scientist, turns out to have to have a tragic backstory, where he was originally trying to use his inventions to do good. That is not referring to Lex Luthor, it is referring to Doctor Sivana, arch-enemy of Captain Marvel. This was revealed in Whiz Comics #15, from 1941.
Speaking of Luthor...In 1939 Superman gained a bald arch-villain. His name? The Ultra-Humanite. Lex Luthor was created in 1940, and his signature Bald of Evil look didn't appear until later. (In fact, the change in Luthor's design is believed to have been an accident.) The Ultra-Humanite himself may be based of a short story made by Superman's creators in 1933, titled "The Reign of the Superman",.
Ever heard of that superhero who has mechanical bracelets full of web fluid and uses them to shoot web lines to swing around on and catch bad guys? Of course I'm referring to Fox Features' The Spider Queen, first appearing in September, 1941.
Many people think, incorrectly, that Wonder Woman was the first female superhero. Actually, there were dozens of female superheroes prior to Wonder Woman. One of the earliest is Ritty, who debuted in late 1939, two years before Wonder Woman. In fact, Wonder Woman isn't even the first female patriotic superhero. She was preceded by USA, Miss Victory, Miss America, Miss Patriot, Pat Patriot and War Nurse.
The earliest (comics) superheroine quite probably is Olga Mesmer, the Girl with the X-Ray Eyes, who appeared in a back-up comic series in the pulp magazine Spicy Mystery Stories starting in August 1937. That's right, she got into print before Superman. Olga Mesmer also was super-strong and the daughter of an alien queen (belonging to a subterranean race that originated from Venus), but her feature only lasted a little over a year. Considering the title of the magazine in which she appeared, it probably no surprise that Olga did not fight in a colourful costume, but mostly in her underwear. Fun fact: Both Spicy Mystery Stories and Action Comics were published by Harry Donenfeld.
You might think that having Cyclops (mutant terrorist) on the cover of Rolling Stone in All-New X-Men was a reference to the controversy surrounding Rolling Stone's "glam Boston Bomber" cover; however the first comic where it appeared came out at least six months before the actual bombing, much less the magazine cover.
When Pacific Rim was released in the UK, Judge Dredd Megazine reprinted Detonator X. Cue indignant fan letter complaining about how Guillermo del Toro didn't acknowledge his inspiration from a little-known British comic, to which the editor replied that giant robots fighting giant monsters had been a mainstay of Japanese monster movies for decades.
Most people think Barbara Gordon was the original Batgirl, and more comic book savvy people will say she was created for the 1966 Batman show. There was a Batgirl five years before Babs, though Betty Kane was written as "Bat-Girl" and was a Distaff Counterpart to Robin even more than later Batgirls.
The Avengers, or an Avengers-like team, is assembled by S.H.I.E.L.D. to help stop villains instead of forming on its own. Sound familiar? Granted, it's regard by most fans as a Dork Age and hence most have chosen to forget about it, but Heroes Reborn, which saw print in 1996 was the first to use the concept of S.H.I.E.L.D. being the ones to bring together the Avengers, five years before The Ultimates did it and 16 years before The Avengers movie used it (and that was likely borrowed from The Ultimates).
An aircraft pilot named Hal Jordan, appearing in a superhero comic book? It happened in a Golden Age Timely/Marvel comic book starring Sub-Mariner, in 1945. Coincidentally (or not), his look is very simiar to his more famous namesake's, who showed up 10 years after.
Underground Comics: Often associated with Robert Crumb, though he wasn't the first artist to drawn comics tackling sexual and political taboos. Jaxxon's "God Nose" (1964) is seen as the oldest example. And in the 1930s and 1940s anonymous comic strip artists made pornographic parodies of well known comic book characters, nicknamed "Tijuana Bibles".