During the stewardship of Cirion, Gondor was attacked by Easterlings and its allies couldn't or wouldn't help them. The Stward sent a last-ditch plea to northern horse-warriors called the Éothéod. While the Éothéod were on friendly terms there was no formal alliance and things were so bad that the Gondorians had given up hope already. That is, until Eorl the Young showed up with just about every Éothéod warrior just in time to save Gondor from being overrun. The Steward granted the Éothéod the (mostly...) unpopulated northern lands in gratitude, and the Éothéod became the Rohirrim. One condition of the grant was that Rohan would aid Gondor whenever they were needed (and vice-versa, although the one time Rohan called for aid, Gondor was busy and couldn't come).
This event means that in the War of the Ring, Gondor and Rohan are formal, treaty- and oath-bound allies. The only factor creating doubt about whether Rohan will answer Denethor's call is the fact that they've just finished fighting another war and are exhausted and concerned about threats to their own realm. Denethor has also called for aid from Gondor's outlying provinces (such as Dol Amroth), lit the beacons long before Gandalf got there and sent a messenger to Rohan to hurry them up. The problem with reinforcing was mainly that said provinces and Rohan were pretty far away, and most were unable to spare more than a tenth of their forces—Rohan went above and beyond the call with the amount of troops they brought, on the thought that if Sauron beat Gondor there wouldn't be much point defending their borders anyhow. (And also honor and stuff.)
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. Nearly every single wizard aligned against the Death Eaters arrives at the battle towards the very end. And the centaurs. And even the house-elves (whom Ron Weasley refuses to ask for aid because he won't issue a request to fight and possibly die to a species incapable of refusal. In the end, one of their own does the recruiting).
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.
The Night's Watch of A Song of Ice and Fire for the first 3 books keeps asking the realm for help against the wildlings, and possibly even worse threats beyond The Wall. They were sure Eddard Stark would answer the call before he was executed. The Watch finally sends ravens after the great ranging ends in disaster, only Stannis Baratheon came to help.