The massive success of Batman Begins and Casino Royale, Darker and Edgier reboots of worn franchises led to a trend of failed or declining franchises being rebooted with varying degrees of success.
The ultimate example, perhaps, is Star Wars, which launched the science-fiction craze of the late 1970s/early 1980s. It pretty much 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.
This is also the reason that Star Trek: Phase Two, a new show that would take up from where Star Trek: The Original Series left off, was cancelled in favor of big-screen Star Trek films.
What's especially amusing about Phase Two is that the Redesigned Enterprise was initially designed by the same people who worked on the designs in Star Wars, and thus looked like some unholy fusion of the Enterprise and a star destroyer, before star wars was even made.
The original Star Wars film itself drew from many sources. The Hidden Fortress connection is well known. The Dune-Tattooine 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."
And let's not forget how 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.
Empire also spawned some trends regarding how sequels are made. At the time, the expectation for any sequel was that it would just rehash the first film, a trend which is sadly still pretty common. Thus, it was rather shocking to have a sequel in which The Bad Guy Wins and the story concludes with a Cliff Hanger. Nowadays, it's downright expected that the second installment of any franchise will end with a cliffhanger, particularly if a third installment is guaranteed. Another trend started by Empire is making the sequel Darker and Edgier in order to keep the premise fresh, which is seen in Indiana Jones and the Temple of Doom and The Lost World: Jurassic Park.
Two years before that, Jaws begat the concept of the Summer Blockbuster, along with a slew of "animals attack" movies; one of the first and best copiers was Alligator.
Spielberg's first movie Duel, while not as influential, has inspired a few ripoffs as well; the recent video-release Joy Ride: Dead Ahead was painfully blatant in its copying.
For that matter, it inspired the Web Original series Marble Hornets, which has itself inspired a bevy of imitators.
Top Gun led to several imitators, from Iron Eagle to the short-lived TV series Supercarrier, as well as a mini-boom of air-combat video games.
Friday the 13th initiated the 1980s' slasher genre; the film was itself preceded by Halloween. Later, Scream re-invigorated the genre; among the works that came in its wake were Halloween H2O and Freddy vs. Jason.
The success of X-Men, followed by the great success of the Spider-Man film franchise, unleashed a deluge of Super Hero-inspired live-action movies upon the world that hasn't let up yet (and probably won't, thanks to the runaway critical and commercial success of Iron Man and The Dark Knight).
Jacques-Yves Cousteau's The Silent World became the nature documentary all other nature documentaries would imitate.
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".
Dark City (1998) created a wave of dark, philosophical Science Fiction movies that question the nature of reality and have lots of John Woo-style gunplay. It was The Matrix that became the most successful and iconic of these films, even though it was not the first. Other examples include eXistenZ,The 13th Floor, and Equilibrium.
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 and video games 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, basically 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 eXistenZ, and, of course, The Matrix. This may have simply been the spirit of the age, however, and not strictly an example of this trope.
Shaft became the model of a film genre for movies targeted towards urban African Americans now otherwise known as Blaxploitation. It also owed a lot to Sweet Sweetback's Baadasssss Song, which wasn't quite an exploitation film.
In a rather strange example, there was an entire genre (Our Man Flint, The Man from U.N.C.L.E., Modesty Blaise, Austin Powers, Spy Hard, Johnny English, etc) parodying spy movies in and/or of the 1960s... except that they only ever seem to parody James Bond. It's as if other spy fiction simply didn't exist, although they don't really need to parody those: the general public know about James Bond most and the Bond movies created or standardised enough tropes by themselves. What made it rather odd is the James Bond series already started out pretty tongue in cheek.
Gladiator re-started 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.
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 an entire 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).
The success of the Saw franchise (at least the first movie) sparked a rash of torture horror movies, such as Hostel, Turistas, and most recently Vacancy.
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 an atrocious Disneyesque cheapass cartoon movie with singing animals.
Then again, it's unlikely that Alien would have been fast-tracked into production if not for the success of Star Wars, proving that this trope isn't necessarily a bad thing.
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.
Hell, 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).
Also, the success of Godzilla led to many different monster movies all across Asia, including Pulgasari (an obscure North Korean film about a monster made of rice that comes to life and eats metal commissioned by none other than Kim Jong-Il himself), Yongary, Gorgo (which was actually made in Britain and featured on Mystery Science Theater 3000), and everyone's favorite flying turtle. The genre was recently started up again with Peter Jackson's King Kong remake, and subsequently revamped with South Korea's The Host, which was followed by Cloverfield.
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, of course, 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.
The 2005 Brad Pitt and Angelina Jolie vehicle Mr. and Mrs. Smith jump-started a series of fairly mediocre "my loved one is a secret agent and/or assassin" films and as of 2010, critics agree it's pretty much been beatento death.
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 (literally: 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.
In the wake of the mega-grossing Alice in Wonderland and to a lesser extent the success of Wicked (both book and stage musical), a glut of Fairy Tale-based film projects were greenlit, often with a Darker and Edgier take promised. The Onion's A.V. Club has been busy snarking all of them under its Newswire banner.
There's going to be two versions of Snow White! One of them with an Action Girl in shining armor.
A film entitled Hansel And Gretel: Witch Hunters has been announced for 2012.
This might have also caused the creation of the new TV shows Grimm and Once Upon a Time.
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.
To be more specific, Love Actually is a British Romantic Comedy with an all star ensemble cast about various couples in love. Valentine's Day and New Year's Eve pretty much the same thing, only revolving around a holiday and with a lot more A-list stars.
Pirates of the Caribbean: On Stranger Tides features an interspecies romance that features several closeups of long, lingering gazes reminiscent of the Twilight films.
After the movie 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.
