So you're one of a group of farmers whose village is under attack by a gang of remorseless bandits. None of you know how to fight, so you leave to hire a group of warriors who are willing to defend you for the pittance you can pay, plus meals. So you come back with seven guys and... hey, Wait a minute, haven't we seen this somewhere before?
No, you haven't been reading TV Tropes for so long that everything is blending together. This is actually a relatively common plot device. Take the basic plot of a bunch of cool guys + awesome goal + clearly defined personality types + any other overtones of Seven Samurai you can think of and bam! Instant "team on a mission" story!
Because Seven Samurai contains many plot elements which are not exclusive to Japanese culture, it's easy to shift the basic narrative around and still get a workable movie angle. In fact, it's such a classically popular example of a narrative that many filmmakers don't even bother being subtle in the process of Homage- there's a lot more movies out there with exactly seven heroes doing this kind of plot than you'd expect.
The trope title and namers are Seven Samurai (Shichinin no samurai) and The Magnificent Seven, the latter of which is famous for both transferring the Kurosawa classic to the Old West (with Kurosawa's blessing) and being a classic in its own right. (A trivial note: Seven Samurai was originally released in the USA as The Magnificent Seven; the English title was changed to a direct translation of the Japanese title later to avoid confusion with the remake.)
Soul Eater, The main protagonist and their partners form a group of 7. Maka the leader and her partner Soul is the lancer, Black star the big guy with Tsubaki the chick, Kid is the smart guy with two chick partners Liz and Patty.
A three-part story arc in the anime version of Fist of the North Star 2 featured Kenshiro teaming up with a gang of post-apocalyptic cowboys clearly modeled after The Magnificent Seven. Even the group's name, "The Wasteland Seven", is taken from the Japanese title of The Magnificent Seven.
One of the good guys explicitly makes the reference, commenting "I love Kurosawa movies!" when the plan is discussed.
Inverted in Gaogaigar, in the second half of the series the seven most powerful villains show up to challenge the heroes. The fan translation of the series even refers to them as the "Magnificent 7 Machine World Primevals".
Kinnikuman, the Planet Rakka mini-arc. The child-like Choujin Beansman comes to Earth to recruit Choujin to help save his people from the Space Samurai, and teams up with Terryman, Ramenman, Brocken Jr., Puyo Puyo, and Crystalman, with Kin forcing himself into the group. Together, they are the Magnificent Choujin 6!
Kinnikuman: Hey, there are seven of us!
In Naruto the first major arc, the Land of Waves, quickly turns into this plot. Team 7 is hired to act as bodyguards for a cantakerous old man named Tazuna but instead of protecting him from ordinary bandits on the journey home, they discover he has been marked for death by Gatou, a shipping magnate and crime lord, who has taken over his impoverished country and wants to stop Tazuna from building a bridge to the mainland and thus break his economic tyranny, and has hired dangerous ninja assassin Momochi Zabuza and his gang of missing-nin to take him out. It ends with the people of Tazuna's village being inspired to make a stand against Gatou's army of hoodlums.
In One Piece, there are the Seven Warlords of the Sea also known as the Shichibukai in Japanese. Those said seven are pirates who work under the World Government for immunity. However, there are not an actually team, having their own crews themselves.
For a long time, the Straw Hat crew had seven members, now they are nine.
Yu-Gi-Oh! has the Pharao Atem and his six Millennium Guardians. These seven were holder of the seven Millennium Items.
Monster Rancher episode "The Courageous Seven" loosely follows the standard formula. The biggest difference is that the village in distress needs to be protected more from a disaster caused by the bad guys.
The titular Seven Deadly Sins from Nanatsu No Taizai are seven extremely powerful criminals who in order to atone for heinous crimes, became knights for the Liones Kingdom. They were heralded as heroes until they were framed for killing the Great Holy Knight Zaratras, an act which forced them to split up during the chaos. A decade later, the seven are sought out by Princess Elizabeth to stop the Holy Knights who have taken over the kingdom.
Marvel Star Wars (the original Star Wars comic book), where immediately after they finished with the movie, the plot moves on to Han and Chewie leading six other fighters (including wanna-be Jedi Don Wan Kihotay and green carnivorous rabbit-man Jaxxom) in defense of a small village.
Marvel Adventures: Avengers had an issue like this. In accordance with the series's early title theme of altering famous movie titles, this was called The Avenging Seven. It actually did include a little village beset by raiders, had someone travel far with the village's single most precious treasure, had an extended sequence of Training the Peaceful Villagers, and at the end the heroes were paid in three tons of food.
Chris Claremont's Sovereign Seven. The seven in question were aliens, each a prince or princess of his or her homeworld, and each the sole survivor of that world. They banded together to protect the universe (and Earth in particular) from 'the Rapture'; the event that destroyed their homeworlds.
The ABC Warriors - they are even referred to as 'The Mek-Nificent Seven', both in-story and by fans.
Demon Knights: Writer Paul Cornell describes the book as "the medieval Magnificent Seven". #3 is titled "The Malificant Seven". Subverted by the end of the first arc - the village they were protecting is rubble, there are few if any survivors among the villagers, and the heroes' "victory" is that they live to fight again.
Films — Animated
A Bug's Life, where Flik the ant recruits a group of what he thinks are warriors to protect his colony, only to later realize that they're just circus performers.
Arthur and his six Sarmatian knights in the 2004 King Arthur movie, with the Britons and the "Woads" as the villagers and the Saxons as the bandits. The scene after the battle of Badon Hill with the graves of the knights who fell is lifted straight from Kurosawa.
In the 1979 movie Seven (not be confused with the 1995 serial killer movie), seven hitmen are hired to kill seven mob bosses who planning a criminal takeover of Hawaii.
The Star Trek: Enterprise episode "Marauders" (especially given that there are seven main characters in this series) with a human mining colony being taught to fight against Klingons who are extorting their deuterium fuel.
Even more obviously, Star Trek: Deep Space Nine had "The Magnificent Ferengi". And it is funny as hell! Though technically, there's only six of them and they don't protect a village, they still engage in the classic "building up the team" and having each character be introduced with a particular character archetype, as well as the obvious Shout-Out in the title.
The "Heart of Gold" episode from Firefly. An interesting twist is that the "Village" to be defended is a whorehouse.
Inverted in The Black Adder episode "The Black Seal" as Edmund gathers the six most evil men in England (plus himself) to take over the kingdom.
Kung Fu: The Legend Continues had an episode called "Dragonswing", where Caine and Peter assemble a team of Shao Lin alumni to help a friend rescue his girlfriend from the thugs who've taken over his Northwestern town. Robert Vaughn guest-starred as Rykker, a mercenary very similar to his Magnificent Seven character.
"A Fistful of Dwarfs", an article in the short-lived gaming magazine Visions detailing a "spaghetti Western" area of the Discworld, included this scenario. This being Discworld, of course, the villagers have a cast-iron contract for the warriors to sign, which specifies that warriors who die don't get paid and exempts the villagers themselves from the nastier bits of the movie.
The Fifth Edition Warhammer rulebook included suggestions for a 'Seven Knights' scenario, in which one player took seven Hero Units against an entire army on the other side.
In that edition of the game this amounted to a ridiculously easy win for the heroes unless the other player got lucky with the artillery.
Meanwhile in Warhammer40000, The Farsight Enclaves supplement for the Tau includes seven special characters that can be taken in place of Farsight's generic bodyguards, each with their own backstory. The fan nickname for them is the Seven Samurai. The book also contains a special scenario similar to the above-mentioned Warhammer ones, where a Tau army consisting of nothing but Farsight and the seven defending an outpost against an endless horde of Tyranids.
The Seven Samurai is actually based on the third play in the Oedipus trilogy by Aeschylus, Seven Against Thebes, making this one Older Than Feudalism. Although this is also an aversion in that the titular seven brought his own army, they were attacking the city during a civil war, and very much painted as the villains in contrast to the city's defenders, who the play focuses on (and whoa are also seven, and thus qualify for this trope. Confused yet?).
The video game Seven Samurai 20XX. Written by Kurosawa's son, hated by damn near everyone.
Bioware likes this trope so much that they built the party members of Mass Effect after it. Shepard is The Hero and The Leader. Kaiden is the Lancer. Ashley is the big guy. Liara is the smart guy. Wrex is the Old Guy (he is a couple hundred years old). Tali is the young guy. Garrus is... whatever's left.
If you see Tali and Liara as both being Smart Guys in different fields, then Garrus could be the Young Guy. Shepard becomes his mentor, after all, and his character development reflects what he picks up from your own behavior as a Paragon or Renegade.
The bulk of Mass Effect 2 is basically assembling an entire 10-person team (12 with the DLC) Magnificent Seven-style, with the added wrinkle of getting said team loyal to you and upgrading your ship and weapons before the main mission of going through the Omega-4 Relay. Though it is possible for people to die during the Suicide Mission, your primary goal is to take out the Collector base and bring everyone back alive.
Halo: Reach has some shades of this. Except it doesn't end very well...
Wakfu's fifth episode does exactly this, down to the title ("The Magnificent Five"). Though, to be honest, it actually is more of a parody of this trope, subverting most plot points common to other examples (the ending, for one).
Justice League: Crisis on Two Earths involves the six 'core' Leaguers (the same from the series, less Hawkgirl, and with Hal Jordan as Green Lantern) join an alternate universe Luthor to save said alternate universe from evil versions of themselves.
Kappa Mikey has an episode where the five crew members are called by a little boy to save their playground from a garbage man intent on turning it into a landfill. The boy is under the impression that they are heroes instead of actors, and the LilyMu crew is under the impression that it's all a publicity gig!
Samurai Jack does this one solo in a jungle-set episode. Jack meets a friendly bunch of high-jumping simians who share food with him, and are then attacked by a rival group of apes. Jack drives them off, and teaches the friendly apes to defend themselves with bamboo staves, in exchange for lessons on how to "jump good."