She then gets apprehended by Doof-2, and is sent to jail. But, Jeremy-2, Phineas-2 and Ferb-2 bust her out.
Next, in the film's climax, Perry comes to the aid of his fellow animal agents fighting off Doof-2's Mecha-Mooks. Phineas rescues Perry afterward. Finally, the kids come to their aid, using almost all of Phineas and Ferb's previous inventions.
Subverted for laughs in "Jungle Jam"; Tom and Jerry seem like they're going to be rescued from the cannibals cornering them on the beach; but as soon as their leader sees who they're rescuing, he immediately does a 180 with the rest of the navy, leaving Tom and Jerry to wing it and swim for their lives under the fire of the cannibals spears.
In "Rough on Rats", two of the kittens save their third sibling from an evil rat this way.
In "Along Came A Duck", the frog saves the duck he was messing around with from drowning, as his shenanigans got the duck tangled in seaweed underwater in the first place.
Molly Moo Cow pulls this to save Robinson Cruesoe from a tribe of cannibals in "Molly Moo Cow and Robinson Cruesoe". She swims back to the island after Robin had scared her off, and grabs all of his rifles with her tail and uses them to scare off the cannibal tribe.
Beast Wars has too many of these to list, generally set up by cutting to the good guys headed towards where they're needed, then cutting back to their destination and letting a scene play out until it's a good time for it to be interrupted by weapons fire. The best example of the trope occurred in "Coming Of The Fuzors, Part 2", when the Maximals are outgunned and surrounded. When it looks like they're done for (Megatron says, "Finish it."), the wall of the Maximal baseship blows open to reveal the new-and-improved Optimus Primal, Back from the Dead and ready for a fight.
Transformers: Full of moments like these, mostly when a character is either first introduced, or appeared to be at death's door previously. One of the best examples has to be the episode "Key to Vector Sigma" where Menasor has Superion pinned and is about to impale him on a large spike - only for Omega Supreme, nearly destroyed earlier in that episode, to show up and KO him.
In fact, Optimus Prime's entire fight scene against the Decepticons and Megatron from the 1986 Animated Movie is a Big Damn Heroes moment. This is acknowledged when Kup says "Optimus did it. He turned the tide".
Also from 1986 Movie: when Hot Rod and Kup are almost being devoured by lots of sharkticons, the Dinobots (and Wheelie) arrive in Dynamic Entry, save their autobot friends and turn the sharkticons against their masters, the Quintessons.
"The Boiling Rock" has Mai saving the group from having the gondola they're in dropped into the boiling lake.
In "Sozin's Comet": Sokka and Toph are about to fall off an airship, and are surrounded by Fire Nation soldiers...in comes Suki, riding on top of another airship, giving them someplace to jump down to and destroying the first airship at the same time.
If Appa is not with the group in a battle scene, then when he shows up it is guaranteed to be a Big Damn Heroes moment.
Zuko also saves the Gaang from Combustion Man, the very assassin he hired to kill them at the beginning of the season, which helps show (most of) them that he is making a genuine attempt to atone for his past actions.
Later that season, when most of the band is captured by an evil sentient robot with a bomb inside it, and Ofdensen is powerless to help (possibly), Pickles pulls this trope off after resolving to Take a Third Option to fall off the wagon and save the band at the same time.
"I AM BACK MOTHERFUCKER!"
In an episode of Rocky And Bullwinkle Bullwinkle refuses to put out the fuse of a bomb until the last moment because "Heroes always arrive in the TA-DA! nick of time."
Bunnies get to be Big Damn Heroes in Watership Down, when Hazel and his runners lure a Big Damn Dog to the warren, just in time to save Bigwig's life by decimating Woundwort's troops.
Batman: (Completely Deadpan) Batman to all points. I could use some air support. Since I can't fly. At all...Now would be good.
Another one happens in the episode "The Secret Society", when Batman is facing five supervillans after tracking down Clayface to a factory.
Clayface: You didn't think I would come here without reinforcements, did you?
Batman: Wish I thought of that. (Garage door falls down, revealing the rest of the members) Oh, wait, I did.
This happens a lot in Jonny Quest. One example would be in Manhattan Maneater, when an amoral hunter is about to shoot a white tiger. Just before he pulls the trigger, a gangster steps in the way and refuses to back down. And another happens not a minute later, when the tiger leaps to attack - only to be shot by a tranquilizer, thanks to Race and Dr. Quest who just made it to the scene.
In the 1982 animated film Heidi's Song, Peter the goatherd and his animal friends crash their way into the basement as Heidi is fighting off the rats. Complete with the "That's What Friends Are For" melody playing in the background, no less.
Bob in ReBoot gets to do one of these right when the Web Riders are about to slaughter everyone on the Saucy Mare. But instead of fighting the Web Riders he orders them to stop, having gained their trust offscreen.
Teen Titans: Way, way too many to list, considering it's a show about heroes. There are a few notable moments, however:
Red X, of all people, has one of these when he shows up out of nowherejust in time to prevent Robin from falling to his death by snatching Robin out of thin air and tossing him to safety on a catwalk.
Believe it or not, Scooby-Doo gets one in episode 10 of Mystery Inc. He rescues Velma and Shaggy from a demonic robot dog by beating it senseless with a forklift. Think about that for a second. Scooby Doo beats a robot dog that would make the terminator proud to a pulp with a forklift. Words cannot describe how awesome it is.
Possibly a nod to Shaggy and Scooby's Big Damn Heroes moment in Scooby Doo and the Alien Invaders.
Green Lantern: Emerald Knights: The entire Corps is collectively moving a planet toward their enemy using all their willpower, but it's not enough. And then, who shows up via portal but the Green Lantern who "doesn't socialize": Mogo who is not only a Green Lantern but a living planet. Heroes don't get much bigger than that.
And again in "The Song of the Petalars", when the cats look hopelessly outnumbered and about to die, who should arrive to say them but Panthro in the Thundertank. Made even more awesome by the fact that he was declared as a dead hero is the opening episode.
Code Lyoko is the epitome of this. They're five teenagers fighting against an evil AI who wants to rule the world and can virtual monsters into the real world.
Super Friends had a story where a time traveling alien was forced by the Phantom Zone prisoners to take them to Superboy's time to kill him. They are nearly successful until Superman and Green Lantern suddenly appear out of nowhere to stop them; it turns out that as soon as the alien was freed, he alerted the Super Friends about what their enemies are attempting and guided them to the proper time to intervene.
Madagascar pulls this THREE TIMES IN A ROW to save Marty from the fossa.
First, Gloria and Melman swing in, complete with Tarzan yell:
Then, the penguins, aiming A FLARE GUN at the fossa:
Skipper: Fossa Halt.
And finally, Alex himself, though it's subverted for a second:
In a Spongebob Squarepants episode, the titular sponge gets rescued from several fish competing to have him as their employee by a masked figure in a Krabby Patty suit. In a Big Damn Anti-Heroes moment, it's Squidward.
Amusingly enough, in the first episode it's Muriel who saves Courage in "A Night at the Katz Motel".
Eustace manages to save the day at least twice: in "Klub Katz", Eustace (turned into a living wrecking ball) realizes Katz has stolen his beloved armchair and flies into a rage, attacking Katz and giving Courage and Muriel time to escape; at the end of "Mission to the Sun", he flies by the sun on a passing comet and gives Muriel and Courage a ride back to Earth.