Mostly they wanted some sort of funny talking animal, but Miyazaki films aren't exactly known for those, so they let him go off at times when Jiji never said anything at all in the Japanese dub; it's not a total distraction, but it takes away from the more quiet mood the original dub gave.
Likewise, John Ratzenberger's performance in the English dub of Spirited Away.
Something similar happened in the English dub of Super Android 13. Androids 15, 14, and the titular form of Android 13 originally did not speak most of the time in the Japanese version (the only words ever spoken by either of them being Son Goku, and in the case of 15, Trunks). The dub actors evidently ad-libbed a large amount of the dialogue.
Cogsworth in Beauty and the Beast originally just mentioned flowers and chocolates when advising the Beast about what present to give Belle. David Ogden Stiers ad-libbed the line "Promises you don't intend to keep."
Iago in Aladdin, when preparing to abandon the palace with Jafar when their treachery was exposed, mentioned packing up guns, weapons knives, as well as a miniature picture of Iago and Jafar that he thought he was making a weird face in. According to the DVD commentary, the entire thing was Iago's voice actor, Gilbert Gottfried, ad-libbing.
According to the DVD Commentary, while Iggy Pop was recording the "voice" of the Eldritch Abomination at the end of the 1983 animated feature Rock & Rule, he actually dropped the microphone, but didn't miss a beat and worked it into his performance.
The 2006 film Hoodwinked! - when Boingo has Red tied up, and is issuing orders to the ski team members, he stops on Keith, the Odd Name Out, and says, "Darnit, change your name! Please? That's not scary! And I'm embarrassed to say that. 'Boris'. Try that. (cue Boris walking away) Keith! Oh, 'Watch out for Keith!'" This part was ad-libbed by Andy Dick, who really thought "Keith" was a stupid name for an evil henchman.
Albeit it's kind of ironic: the names mean almost the same thing in different languages. Keith is Scottish-Gaelic for, "from the battlefield". Boris is Slavic for, "battler, or, warrior".
As was B.O.B.'s line "I think that jello gave me a fake phone number" which was completely made up on the spot by Seth Rogen.
In Atlantis: The Lost Empire, Michael J. Fox's character, Milo, is vomiting over the side of a ship; under his breath he mutters "Carrots, why is it always carrots? I don't even eat carrots...", which was an ad-lib. Also, apparently Jim Varney (who played the vegetable-allergic "Cookie") improvised a lot of his lines. The directors explained that they could bring him in for maybe five lines but would schedule for four hours because everything he came up with was solid gold.
In The Road to El Dorado, voice actors Kevin Kline and Kenneth Branagh were put together in a single "voice box" so that they could bounce off of each other (voice actors generally aren't given this option). This naturally led to a good deal of ad-libbing from both (think the "loquacious" line from their opening "duel").
When Osmosis Jones comes back from "The Zit" he greets Leah by saying "Brandy— oh I mean Leah". Brandy Norwood was the voice of Leah. The error was left in because the director thought it was funny.
The cast from Twice Upon a Time was composed of improv actors, and as a result the movie has several "alternate" versions, including one with language that was very much not suitable for children.
For the voice acting of All Dogs Go to Heaven, much like the instance of The Road to El Dorado, as mentioned above, Burt Reynolds and Dom De Luise were put in the same sound booth to record their dialogue, and as a result, much of the back and forth between them was improvised.
In The Princess and the Frog, the line "That's new" (as in, right after Naveen has attempted to woo Tiana, only to have his throat balloon like a frog) was supposed to be spoken in a confused, surprised way - "Whoa, that's new." But instead, the actor voicing Naveen said it suave, and it got into the film that way. It works.
From The Lion King, Timon's line "What do you want me to do, dress in drag and do the hula?" was an ad-lib by the voice actor. The line ended up spawning a scene where Timon's 'idea' causes an infamous Gilligan Cut.
Similarly, during "Be Prepared", you might notice that Ed is uncharacteristically speaking (or rather, singing) in the song. That's because Jim Cummings, Ed's voice actor, was filling in for Scar for the remainder of the song at that point, because Jeremy Irons, Scar's regular voice actor for the film, was unable to sing the song anymore due to blowing out his voice at the verse "You Won't Get A Sniff Without Me!"
In How to Train Your Dragon, the line "thank-you for nothing, you useless reptile", was an ad-lib by Jay Baruchel. The trivia track on the disc also notes other places where voice actors improvised.
In Shrek, there's a scene where Donkey chastises Shrek for belching, saying it's no way to behave around a princess - which is then followed by Fiona unleashing an impressive belch of her own. Fiona's belch was real and unscripted - Cameron Diaz had been drinking Coke while recording her lines. She stayed in character, and Eddie Murphy improvised the next line, "She's as nasty as you are!" and it was kept in the final take.
Mike Myers also improvised the line "You're on your way to a smacked bottom" after getting annoyed at one of the directors.
The inclusion of "All Star" by Smash Mouth was also a Throw It In - it was originally intended as a placeholder until a better song was found, but test audiences loved it, so it was kept in the final version. This also led to the producers asking Smash Mouth to do a cover of "I'm a Believer" for the end of the movie.
Strange, since the end credits feature a Suspiciously Similar Song, "Stay Home" by Self, which would have fit the opening scene perfectly.
In Kung Fu Panda, Po's father owning a noodle shop was incorporated into the film after the producers found out that the voice actor for the character also owned a noodle shop.
When recording voice tracks for the animated film Madagascar, the animators did temporary voice tracks, which were then to be dubbed over by celebrity voice actors. They had originally planned for Robert Stack to voice Skipper the penguin, but after he died, they just left animator Tom McGrath's voice track in because he'd gotten so into playing the character. This may also be why Kowalski and Private are voiced by DreamWorks staff (but Rico is voiced by John DiMaggio).
King Julien's entire character was almost entirely thrown in. He was originally an extra with only three lines, but when Sacha Baron Cohen start ad-libbing in an over-the-top Indian accent at his audition, the producers found it too good to leave out. Even then, many of his lines are improvised (such as his quip about the gecko on his crown, which prompted to animators to add said gecko).
The same thing happened on The Incredibles. Originally, Bud Luckey and Brad Bird did the voices of Rick Dicker and Edna Mode as temp tracks. Lily Tomlin was at one point considered for the part of Edna, but she said "What do you need me for? You got it already." after hearing Brad Bird's performance.
In Sita Sings the Blues, there are three narrators. The original screenplay called for none. These three people were originally being interviewed for their take on the story. The discussion was so interesting, that Nina Paley added narrators, so she could use it.
The squirrel in The Emperor's New Groove was a gag drawn on the original storyboards. They crew liked him so much he was put into the movie and even ended up as a plot device.
Miss Spink and Miss Forcible's song in Coraline was originally written as a placeholder, with the intention of having They Might Be Giants compose a proper song for the scene. Linnell and Flansburgh came in, heard the placeholder song, and said it sounded good enough to them.
In TMNT, while Raphael is fighting the Jersey Devil, a fridge falls over on the monster, and the background music goes silent for a moment before he bursts out again. That moment of silence was a mixing accident, according to the commentary.
The whole scene in Treasure Planet with Jim and Silver trying to get Morph to bring them the map was ad-libbed.
During a recording session for Brother Bear where Joaquin Phoenix and Jeremy Suarez recorded their dialogue together, Phoenix messed up the line "your friend Bucky" as "your friend Binky". Suarez corrected him with, "First of all, his name's Bucky, not Binky and it wasn't a pine-cone it was a pine-nut! And it was huge! Even bigger than your fat head!" This ended up in the film.