Nice Kitty...

Every now and then The Hero runs across a big animal he would rather not disturb. It's a bear, or a tiger, or Cerberus.

Correct procedure is to back away slowly, making placatory sounds such as 'Niiiice kitty... good kitty..." then run just before the pounce.

Occasionally the Kitty turns out to be an actual Nice Kitty, and acts like a giant puppy.

Anime and Manga

 * Complete inversion on Azumanga Daioh: The animal is tiny, not big; the character approaches it while placating it instead of backing away, and instead of it turning out to be nice, it turned out to be exactly as dangerous as it didn't look.

Film

 * Disney's Aladdin. As can be heard here, starting at 8:10, Aladdin says "Down kitty...Look! A mouse!...Scat...C'mon, good tiger... Take off and go!...Down kitty".
 * By the way, the "Good tiger... Take off and go!" part is one of the movie's most infamous Mondegreens.
 * Mike in the Teaser Trailer for Monsters, Inc.: "Nice doggy. Nice big doggy."
 * You think Tim Allen's character is going to do this when he sees a dog in his first foray as Santa in The Santa Clause, but he subverts it: "Nice... teeth!"
 * In Octopussy, James Bond commands a tiger to "Sit!" (in Barbara Woodhouse's distinctive tone). And it does.
 * In Ghostbusters when Louis Tully is confronted by the monstrous Vinz Clortho, he tries to soothe it with, "Good doggie...nice little pooch..."
 * The titular lion in Secondhand Lions. Definitely a very nice kitty, she is impossibly tame, though very protective of her cub (Walter).
 * Pee-wee's Big Adventure - stranded in the middle of nowhere in pitch dark, Pee-Wee hears nearby growling and nervously goes "nice kitty..." When he turns on a light, he finds himself surrounded by big predatory animals that absolutely don't belong in the American desert southwest.
 * "Nice doggy, nice doggy, roll over, play dead!"

Oral Tradition
""Diplomacy is the art of saying 'nice doggie' until you can find a rock.""
 * There's an old saying that goes:

Video Games

 * In a King's Quest V death, Graham says "nice birdie" to a roc hatchling about to eat him.

Western Animation

 * A subversion in The Flintstones: Barney sees a Bantydactyl and cheerfully says "Here, pussy pussy" to it until it cheerfully opens its mouth and grabs him leaving only his feet exposed.
 * I know I've seen this on The Simpsons with Homer doing a Phil Silvers-esque voice, but I don't know if Phil Silvers himself ever did it or not. (Or Top Cat, who was based on Silvers.)
 * Avatar: The Last Airbender: Aang flees a big horned gorilla thing until he realizes it's King Bumi's pet. Then he tentatively asks, "...Flopsy?" To which Flopsy responds by grabbing him and cuddling him.

Web Animation

 * In Yu-Gi-Oh!: The Abridged Series, Bakura tries that offscreen with a tiger. Doesn't help, obviously.