Rango has the titular character calling upon the aid of the family of mole hillbillies that had previously tried to kill him several times.
Mother mole: You got some nerve showing up here.
Rango: Your boys are about to be hung for a crime they didn't commit. (beat) But I have a plan.
The Lion King: during the climactic final battle of the movie, Simba is headed to Pride Rock, to face Scar alone. As soon as he takes his first good look at his rightful home, he is shocked to see the devastation that has taken place during his absence. Cue Nala walking out of the fog, telling him that this is what Scar has done to the once-majestic Pride Lands, soon thereafter offering her help. Simba initially refuses, rather vehemently, but then Timon and Pumbaa emerge, backing Nala's claims and addressing how grim the situation is, and offering their servitude. Simba then accepts, dashing off to go confront Scar and reclaim his land. As said actual battle progresses and more and more of the major characters are freed, Rafiki, Zazu, and the pack of lionesses charge in to help Simba.
The Twilight Bark sequence in 101 Dalmatians; usually only a gossip chain, as lampshaded by Perdita, it is repurposed for this to find her and Pongo's stolen children.
The Rescuers Down Under has one hell of an example where, upon learning of a young boy's kidnapping, members of the Rescue Aid Society relay for help to their base in New York from Australia. The signal is sent first from a ramshackle broadcasting station in the outback, then from the juryrigged wreck of a P-45 fighter in the Marshall Islands, then from there to a high-tech American Intelligence listening post in Hawaii, which the RAS has apparently hacked into, and then (whilst we don't see the rest of the stations) it jumps from San Francisco to Denver to Chicago to D.C. before finally arriving in New York. ...oh, and did we forget to mention that the RAS is an organisation made up of mice?
In WALL•E, after the titular robot is crushed to keep the Holo-Detector from closing, EVE desperately cries "PLANT!" to the crowd of humans and robots gathered on the Ledo Deck. MO finds the tiny sprig, and both the people and the robots work together to pass the greenery to her.
Live Action Films
In Army of Darkness, Ash calls upon Duke Henry the Red, last seen about to be put to death by Arthur, to help defend the Necronomicon from the Deadites. And while he does show up fashionably late, he does eventually bring his armies to Arthur's castle to assist.
Avatar uses this twice. First, Jake Sully uses his new position as Toruk Makto to summon other Na'vi tribes to fight the RDA who seek to strip their home moon dry. Second, Eywa, the mother goddess of Pandora herself summons the Pandoran wildlife to reinforce the united Na'vi army just as their about to be wiped out, winning the battle. Bottom line, don't fuck with Eywa.
In Breaker! Breaker!, Arlene manages to escape from Judge Josh's goons and find a working CB radio, which she uses to put out a desperate call for help, as JD (Chuck Norris) is about to be killed by the town's corrupt police. Cue every trucker in hearing range - all of whom presumably are friends of JD's and/or were screwed over by Judge Josh and his minions - massing into one giant Convoy of Destruction massive enough to make the ground shake at their approach. Of course, thanks to the film's limited budget, this was about seven or eight older trucks. Still enough to knock the town flat, though.
The same thing happens in the 1978 film Convoy. When a trucker named Spider Mike leaves the eponymous convoy, he gets arrested and beaten in Texas by a sheriff, working with the main antagonist of the film. The janitor of the local jail gets on the CB to call for help and various truckers pass the word to the leader of the convoy, Rubber Duck, who heads out to rescue him. The next morning, Rubber Duck and eight other truckers line up outside of town, deliver an ominous, spine-chilling blast on their horns, and wreck the town to free Spider Mike.
Parodied in Duck Soup. Firefly (Groucho Marx) gets on the radio and calls: "Mayday, mayday! Rush to Freedonia! Three men and a woman are trapped in a building. Send more men at once! If you don't have any men, send three more women!" Cue Stock footage of fire engines, police motorcycles, Olympic runners, monkeys, elephants, and dolphins.
Parodied in Fahrenheit 9/11 when Michael Moore lists the names of the countries that answered US calls for aid in defeating Saddam Hussein, whether or not they had a military.
Happens all the goddamn time the Godzilla series whenever the military can't handle a monster and calls another monster to help them. Perhaps the most notable example can be found in Mothra vs. Godzilla (1964). In that movie, Mothra is very angry with Japan for the nuclear testing that trashed her home island and the refusal to return her egg to her, but when Godzilla attacks Mothra shows up at the last minute to help based on some sincere Japanese citizens' pleads for help.
Independence Day gives us a twofer. First, the Air Force recruits any civilian who knows how to fly a plane to fight the aliens, and then this trope plays out on a global scale as the US uses a telegraph to unite the Russians, the Chinese, the Israelis, the Arabs and many other nations into one coordinated counterattack.
In Iron Sky, the US space ship is severely outgunned by the Nazi Cool Airships and desperately calls for reinforcements - promptly provided by everyone but Finland, who have opted for not violating space armament treaties.
In It's a Wonderful Life, when George is on the verge of bankruptcy, Potter snidely tells George Bailey that if he were to ask the "riff-raff" he spent much of his adult life helping for aid when he needed it, they would turn on him. Fortunately for George, Rousseau Was Right, and all those who George had helped over the course of the movie are more than happy to help him.
Spy Kids 3D: Game Over ended with the Cortezes calling on their immediate family, then (in the vein of the running theme of "family") various people they had met over the course of their adventures to fight the Toymaster's robots. The movie's haphazard direction keeps it from the climactic feel it should have, but it's still a highlight.
The Lord of the Rings, naturally. In the film, Denethor refused to light the signal fires due to a combination of bad blood between Gondor and Rohan, and due to a misguided notion that Gondor needed no aid (Denethor being under the influence of Sauron affected his decision making somewhat). Pippin manages to sneak into one of the towers and lights the fire himself. Théoden, when the subject was first broached by Aragorn, was bitter over Gondor not sending any help to Rohan during their devastating fight... when he actually gets the call, though, he personally leads The Cavalry. (Worth noting, in the book, even under Sauron's corrupting influence, Denethor had the presence of mind to send for help before the heroes arrived, and was waiting for the reinforcements.)
The Music Man. During the film's climax, Marian saves Harold Hill from the wrath of the town after his con is revealed by appealing to individual townspeople who's lives Harold improved during his time in River City. One by one the townspeople stand up in support of Harold until the Mayor agrees to relent.
Subverted brutally at the end of Star Wars: The Last Jedi. The entire plot of the film is about the Resistance getting to Crait so they can summon their allies...and they don't respond, leaving the Resistance with nothing but gutted speeders to fend off against the entire First Order.