The Trope Namer is, ironically, not really an example of this trope, because Rohan (and other nations that aid Gondor) are not "unlikely allies", but members of a long-term alliance, and the only factor creating doubt about whether Rohan will come is the fact that they've just finished fighting another war and are exhausted and concerned about threats to their own realm. There's also many other nations - smaller ones than Rohan - which send aid, although only a tenth of their available man-power was sent due to their need to defend their own borders against Sauron's assault; Rohan were the ones who really went above and beyond in terms of providing aid.
Also in the book Denethor is more quick-witted than is shown in the film, and had actually lit the beacons long before Gandalf arrived. "It is over-late to send for help when you are already besieged," indeed. He also sends a messenger to Rohan to request aid, since Rohan is more distant than the other nations.
Not other nations; those were provinces of Gondor itself. Gondor is the nation and the battle was for Minas Tirith, its capital. Gondor is a pretty big country and it took time for the troops from other provinces to get to Minas Tirith, especially given they were also fighting the war.
Another fantasy fiction example comes at the end of Jacqueline Carey's Kushiel's Dart, in which the heroine journeys to Alba (a fantasy version of Great Britain) to convince the Albans to bring their army to the aid of Terre d'Ange (France) which has been invaded by Skaldia (Germany/Scandinavia).
Harry Potter - the climax of The Deathly Hallows, in which the school students, the Order of the Phoenix, estranged members of the Weasley and Dumbledore families, and even Harry's old Quidditch team all turn out to fight.
And let's not forget that nearly every single wizard aligned against the Death Eaters arrives to the battle towards the very end.
And the centaurs. And even the frigging house-elves.
Inverted and subverted in the Star Wars Expanded UniverseX-wing novel Solo Command, when the Big Bad, Warlord Zsinj, calls up every pirate and mercenary he'd ever hired to come and defend his crippled ship. The protagonists are among that number, having successfully posed as pirates in the previous novel. Zsinj's call for help confirms that he is vulnerable, not preparing a trap, allowing the protagonists to go and kick his ass.
This is also a Crowning Moment of Redemption for Shalla Nelprin. During their desperate escape from the Binring Biomedical facility, she had attacked Zsinj's unarmed combat expert in the presence of armed stormtroopers, because said combat expert had recognized her as a member of their fake pirate gang, the Hawk-bats. Since then, she had wondered if preserving the Hawk-bat connection had been worth risking everyone's lives over; this event proved her action to be the correct one.
Subverted in Star Trek: Destiny, where the United Federation of Planets needs to call on virtually every major power in the Alpha and Beta Quadrants for help against an impending Borg invasion. President Bacco hosts an emergency conference and tries to persuade or pressure nine other nations into sending forces to the Azure Nebula alongside Starfleet. Some of them refuse to show up and the fleet is wiped-out in minutes anyway. All that her efforts really accomplish in the long run is to antagonize the Tholians.
The climax of Martin the Warrior, the sixth Redwall book.
At one point in Spider Robinson's Callahans Crosstime Saloon series, a telepathic call goes out to all the Regulars. They respond so immediately that at least one stove is left running, a suicide prevention is called short (they bring him along!), a bomb-tech leaves an active bomb-site (he brings the bomb along!), and even more extreme 'drop-everything' examples.