The Matrix brought Cyber Punk into the mainstream during the late 1990s, when the genre was already almost dead in Sci-Fi literature, and spawned a multitude of movies (I.E. The One) and video games (I.E. Max Payne) which mostly imitated its cinematic style and Bullet Time CGI effects.
Supposedly, when the Wachowskis were peddling their script, they brought with them a comic book and told prospective buyers that they wanted to do something like that into a movie. The comic in question? Ghost in the Shell.
More broadly, Dark City seems to have been the advance guard of a rash of films in 1998-1999 of varying genres involving a closed or false reality. Non-action examples would be Pleasantville, The Truman Show, and maybe even Being John Malkovich. These existed alongside science-fiction titles like E Xisten Z and The Matrix. This may have simply been the spirit of the age, however, and not strictly an example of this trope.
The nature documentary March of the Penguins led to two animated features with penguin characters: Happy Feet and Surf's Up. Both were in production long before March of the Penguins was released (that being the nature of feature-quality animation of either kind), but the success of March probably got them slightly more publicity for getting on the "penguin bandwagon".
Jay and Silent Bob Strike Back actually Lampshaded this trend by joking about Hollywood desperately buying up every superhero franchise in sight in order to cash-in on the success of X-Men. In real life, even obscure properties like Namor were optioned for movies after the success of X-Men.
Going slightly further back, Blade was really the first of the modern wave of superhero movies, as well as the one that popularized the use of black leather in place of gaudy superhero costumes. (At least for modern cinema. Batman was wearing black years earlier in the Tim Burton films). It also proved that comic book movies cold be successful even if the subject wasn't initially familiar to the public at large, which proved a particular boon to Marvel (whose major characters didn't have nearly the name recognition of Superman and Batman pre-2000).
After the success of The Dark Knight, many franchise films, some not even related to comics, have followed suit with a Continuity Reboot and Sequel Escalation set in a world that downplays supernatural or overly "fantastic" elements, focus on the origins of iconic items or costuming and villains are more like terrorists in their actions. Captain America: The Winter Soldier and Dredd in particular seem to be tonally inspired by the Nolan Bat-films.
This goes beyond even comic book movies, with reports of planned linked-film franchises based on King Arthur, Robin Hood, and the Universal monster movies (Dracula, Frankenstein, etc.).
The ultimate example, perhaps, is Star Wars, which launched the science-fiction craze of the late 1970s/early 1980s. It opened the door for expensive fantasy/science fiction movies, and is credited with changing the way big blockbusters are viewed by Hollywood, but most of them were shallow attempts to cash in.
Star Wars is also the reason that Moonraker was made when it was. Originally (in 1977) the next James Bond movie after The Spy Who Loved Me was supposed to be For Your Eyes Only, and indeed the closing credits of the former explicitly state this. The success of Star Wars changed this, and the 'spacey' movie was made. It was mediocre at best, so the next film was far more down-to-earth.
The original Star Wars film itself drew from many sources. The Hidden Fortress connection is well known. The Dune-Tatooine inspiration is pretty obvious. You can tell George Lucas must have seen at least Space Battleship Yamato episodes 26, 1, and 8, in that order, so we can probably pin his famous trip to Japan down to early 1975, when the series went into reruns. Isaac Asimov noticed some similarity to his Foundation series but didn't take it personally. As Wilson Mizner observed, stealing from everybody is just called "research."
The Empire Strikes Back spawned the astonishingly overused cliché of how the villain is the hero's father. The reason it worked in that film was because there was so much talk about Luke's father that the reveal was so surprising and ironic at the time. Nowadays, many writers seem to just throw it in with very little foreshadowing and buildup that it is met with little surprise at the reveal.
Gladiator restarted the Historical Epic genre of things like Ben Hur. Russell Crowe's powerful performance, the high budget settings, and gritty action caught something in the audience that studios have attempted to imitate with films such as Troy, Alexander, and most recently, 300.
While obviously different from other historical epics, films like Gangs of New York also owe a lot to Gladiator, both stylistically and in getting the execs to actually greenlight the massive budgets they needed. Some of these have garnered successes in their own light, not as imitations but as part as a new wave of Epic films.
Before Gladiator in 2000, several sword-swinging period movies were made in the Nineties in the wake of the major hit Robin Hood: Prince of Thieves in 1991. The most obviously derivative is the 1993 version of The Three Musketeers - both movies have a similar light tone, a Laughably EvilLarge Ham of a villain, major liberties taken with both the source material and historical setting, an Award Bait Song by the same artist (plus twoothers later), and even the same cast member playing the top henchman. 1995's First Knight continued the trend with a new take on the King Arthur legend, with Sean Connery as the king (he had a cameo in Prince of Thieves as King Richard). Braveheart, also in 1995, was the biggest historical adventure epic in recent memory before Gladiator, and both won five Oscars in their time. Dragonheart in 1996 was a medieval fantasy with Sean Connery as a dragon. The Man in the Iron Mask in 1998 featured older versions of the characters from The Three Musketeers (but is not otherwise related to the 1993 movie) and was directed and written by the writer of Braveheart.
Soft on Demand, a somewhat infamous Japanese adult video company, created a small series of films called Zenra -X-, where Zenra is the Japanese word for Nude, and -X- is some random everyday activity or sport — for example, Zenra Volleyball, Zenra Cross-town Bus Tour, Zenra Officework, Zenra Orchestra, etc. These films were successful enough and mimicked enough that Zenra has become a genre of Japanese pornography, dedicated to pointless nudity, with little to no sex, and occasional plots. It helps that the Soft on Demand company doesn't take themselves at all seriously.
Night of the Living Dead may have been the first real zombie film, but there were only a few imitators after it, like Children Shouldn't Play With Dead Things and the Spanish Tombs of the Blind Dead series. What really set off the zombie film craze was the release of Romero's later Dawn of the Dead and the Italian-made Zombi 2 (Dawn of the Dead was called Zombi in Italy).
Following the blockbuster success of Titanic, several other movies were made about the Titanic and shipwrecks in general to try to follow in its footsteps. Including twoseparate atrocious Disneyesque cheapass cartoon movies with singing animals. Which just goes to show, some people will try to Disneyfy anything.
Pearl Harbor was also a pretty blatant attempt to recapture the tragic-love-amid-larger-historical-tragedy magic that made Titanic so many gazillions.
M. Night Shyamalan's The Sixth Sense inspired many movies that completely ignored quality, fun, action and plot, instead focusing on some supernatural twist. They ranged from good to bad to terrible. Unusually, Shyamalan himself seems to have been the main exponent of this trend.
Shutter even tries to look like a Japanese remake (the original was Thai, by the way).
After films like Mary Poppins, My Fair Lady, and especially The Sound of Music hit the big time at the mid-1960s box-office, big studios fast-tracked a ton of big-budget movie musicals. While one, Oliver!, was successful enough to win the 1968 Best Picture Oscar, and Funny Girl launched Barbra Streisand's movie career, changing audience tastes doomed the vast majority of them to significant financial losses. The genre limped through the 1970s and quietly died in the early 1980s (with a mini-revival by way of the Disney Animated Canon in the 90s). Only in recent years has the genre become respectable again, and it's still not particularly profitable (in America anyway - the story is a bit different overseas, with Mamma Mia! outperforming The Dark Knight in several countries, notably Britain).
Ironically, screenwriter Simon Kinberg has said that the upcoming Fantastic Four reboot is also heavily influenced by Batman Begins, as it will have a Darker and Edgier tone and a more realistic setting.
The massive popularity of Bruce Lee after his tragic passing led to a peculiar phenomenon known as "Brucesploitation", in which various Hong Kong studios made movies starring Bruce Lee imitators with titles like Bruce Lee Fights Back From the Grave and The Clones of Bruce Lee. The fad eventually died out when none of the imitators were as successful as the original, though one of them, Cheng Long, would later go on to greater fame by pioneering his own unique, often-imitated, never-duplicated style of martial arts film. You might know him as Jackie Chan.
After The Exorcist made boatloads of money for Warner Bros., the rest of the '70s saw a veritable flood of horror movies based around children: The Omen, The Other, Audrey Rose, etc. Many of its successors (such as The Sentinel) also chose to imitate its preoccupation with the symbolism and aesthetics of the Catholic church, as opposed to the scary-little-kid formula; in fact, any horror movie over the last forty or so years that relies heavily on Catholic iconography could be said to be following in The Exorcist's footsteps.
Star Wars is as far away from an imitator of 2001 as you can get, but John Dykstra continued to use 2001's style of lighting and detailing spacecraft on Star Wars, and from there it became the standard way to depict spacecraft in all of visual science fiction.
The book of Solaris though was written 7 years before 2001 came out, and featured themes like inexplicable aliens, almost empty space stations, and isolation from other humans.
Every few years or so, when a movie shown in 3D becomes a hit, many movies after that will premiere in 3D. The most recent example is Avatar. Quality varies on these films. Some movies will be truly enhanced by 3D, others will look nice but can do without it, and others just don't work in 3D. Avatar, which started the latest 3D movement, was considered by many to look better in 3D. The film version of How to Train Your Dragon and Megamind were considered by some critics, notably Roger Ebert, to look nice, but could work just fine without it. And rushed 3D conversions to cash in this trope (3D tickets are more expensive and thus profitable), such as Clash of the Titans and The Last Airbender, weren't well-received, with the latter even receiving complaints that the botched 3D only made a bad movie worse.
While it isn't necessarily the case, the marketing of The Lone Ranger makes it come across as such, promoting the film as from the same people as Pirates of the Caribbean and showing off Johnny Depp as the deuteragonist. Clearly, Disney attempted to catch that same magic. It didn't work.
The success of Sherlock Holmes (which might've been preceded by From Hell) led to similar steampunk-ish disturbed detective works like Poe where Edgar Allen himself helps solve murders based on his stories, and a version of Robin Hood where the sheriff of Nottingham is pursuing a murderous archer he discovers that Robin was framed and the two bring down the real murderer. Unfortunately that story was too different and what we got was Ridley Scott's Robin Hood.
After Project X came out, real life teens spread the news about their own Project X parties on social networking sites, with over 2000 people showing up to most of them. Two of these parties ended in violent shootings. Oddly enough, one teen got a job offer out of it because of his marketing skills.
When adapting Snow Flower and the Secret Fan to film, the writers added a 21st century storyline to parallel the 19th century storyline from the original novel. This was likely an attempt to emulate the success of The Joy Luck Club. They even got Wayne Wang to direct.
Dino de Laurentiis's career as a producer, from the middle of The Seventies onwards, included a lot of movies that were deliberately trying not only to follow but top the decade's blockbusters:
Jaws's success was the basis for three different de Laurentiis productions featuring frightening beasts: The White Buffalo (1976), King Kong (also 1976), and Orca: The Killer Whale (1977). Though his plans to do a crossover between the latter two films didn't come to fruition, he did make a sequel to the Kong remake in '86.
King of the Gypsies (1978) was his answer to The Godfather, focusing on a different kind of underworld.
Hurricane (1979) was an attempt to capitalize on the Disaster Movie craze.
While the use of post-credits scenes was nothing new (not even in this franchise, as X-Men: The Last Stand already did its own), the Marvel Cinematic Universe popularized their use as a tool for 'world-building', i.e. using them to tie non-sequel movies into a bigger universe. The Wolverine "copies" this concept as it contains a Stinger that ties it into X-Men: Days of Future Past, when originally this movie wasn't going to be related to First Class nor the original series.
The Marvel Cinematic Universe has also kicked off a trend of film studios setting all their comic-book films in a Shared Universe. Warner Bros is aiming to create a DC Cinematic Universe by having Batman and Wonder Woman appear in the sequel to Man of Steel. Fox, meanwhile, planned to set their Fantastic Four reboot in the same continuity as the X-Men movies before the idea was scrapped.
Harry Potter and the Deathly Hallows was initially going to be a single film, but it had to be split into two parts due to length of the shooting script (nearly 5 hours long). After the two films had a combined box office intake of $2.2 billion (compared to the $1 billion a single film would have brought in), all the other studios which were working on book-to-film adaptations of young adult novels decided split up the series' final books so they could bring in more profits- leading to two-part adaptations of Breaking Dawn and Mockingjay.