Horo from Spice and Wolf can usually be bought with apples, but will occasionally demand fancier foods (most notably, the honey-pickled peaches that are considered a delicacy in the city they are currently visiting)
In Beetle Bailey, Beetle can get Sarge to excuse him from anything with four simple words: "my mom's homemade cookies".
One case where food is offered as payment happens in Peanuts where Charlie Brown offers to trade players with Peppermint Patty's team, offering Lucy for Marcie. When Lucy complains that he was robbed, Charlie Brown disagrees, saying that he got the better deal because Patty included a pizza. (He was more right than he imagined. When Patty realizes what a terrible player Lucy is, she wants to call the deal off; Charlie Brown tells her, "I already ate the pizza...")
Played with in the fifty-ninth chapter of Kyon Big Damn Hero. After Kyon and most of the girls in the Brigade teleported to Yuki's Pocket Dimension for some training Hanyuu instantly assumed they went somewhere to do "naughty things" and ran off to inform Rika, only to be stopped by Kuyou buying off her silence with cookies. Funnily enough, the "bribing" part only happened in Hanyuu's head as Kuyou only wanted to share some of her cookies with her.
Home Alone 3: The brother's parrot only plays along with the scheme if you have TWO crackers.
"Double, or nothing"
In Strange Brew, Bob and Doug McKenzie successfully bribe the secretary at Elsinore Brewery for information by using a donut: "Perhaps one of THESE would refresh your memory?" She gives them a little information, but holds out for another before giving up the full scoop.
Harry Dresden is known to secure the loyalty of the Wildfae with pizza. It started as a simple quid pro quo: Pizza for information. Now they're his own little personal volunteer army.
In the Discworld novel Night Watch, the narration mentions that the Ankh-Morpork City Watch has been reformed to the extent that they don't accept bribes, except donuts and beer.
In Unseen Academicals Glenda Sugarbean gets in to see Vetinari twice by doing this to the palace guards.
Though they had been instructed to take all bribes offered, bring the people in question to a waiting room, and then lock it until Lord Vetinari decides what to do with them. Unfortunately they also dispose of any food bribes afterwards in fear of poison, which in this case even Lord Vetinari considered a crime against good cooking.
Miles Vorkosigan is known to use Ma Kosti's cooking to bribe people, though this tends to lead to half-joking threats to kidnap her.
Stephanie Plum is often bribed by her mother by food. Seeing as how she is a very good cook and Steph is often broke, it is a very powerful motivator. When regular food just won't do, cake will usually seal the deal.
In one book former hooker Lula has witnessed a murder but is reluctant to go to the police station to make an official statement. Joe finally gets her to go by promising to buy her a bucket of chicken and a Carvel ice cream cake.
In the Tim Dorsey novel Orange Crush, a lobbyist considers the food and drink he provides at campaign functions to be part of the lobbying, with the impact being about ten cents on the dollar (A free meal worth fifty dollars provides as much influence with a politician as a $500 donation to his campaign).
iCarly: Sam can be bribed with food for a variety of reasons. Once, so that she'd leave resident Butt Monkey Freddie alone for a while, and earlier in her life, so that she'd be someone's boyfriend. Both times, the food in question was bacon.
Kel on Kenan & Kel would do anything for a bottle of orange soda.
Power Rangers RPM: In "...And Action", the cast gives the viewers a behind-the-scenes look at the show without actually breaking character. Ziggy has to offer Doctor K sweets to get her involved.
The Amanda Show: Amanda's stalker Penelope Taynt tries to bribe Barney the security guard so she can sneak into Amanda's show. After failing to bribe him with money and jewels, Barney finally gives in when Penelope gives him a Pizza. A very nice slice of Pizza.
In Psych episode "Shawn Interrupted", Shawn needs to get a possibly-insane character in front of a hidden camera in the hospital library, so he uses a bowl of Skittles to do it since he's already seen that they're his Trademark Favorite Food.
In Lost Souls MUD, this is the most pleasant way of getting past Kerberos, the three-headed dog guarding the fiery portal from the cave of Tainaron to the River Tethys.
The Kappa is a fearsome monster that likes to eat human entrails and blood. One way to survive an encounter with one is to offer it the one treat it enjoys more than human flesh: cucumbers. Offering a kappa a cucumber inscribed with your name on it will earn you your safety and maybe even the kappa's friendship.
In The Bible, Jacob was able to get his brother Esau to sell his birthright for a bowl of stew.
In Tsukihime, Shiki regularly uses curry bread to get Ciel to talk to him.
The original The Legend of Zelda features this in the seventh dungeon, as you have to buy a bait to pass a particularly hungry Moblin enemy.
Dragon Age: Origins: Your companions have different ways of getting past the guard to the Circle Tower. Morrigan or Shale will scare the living daylights out of him, Leliana will regale him with stories, and Sten... will offer him sweets (that he stole from a fat kid "for his own good"). Truly, Templar discipline is to be feared. It's less funny when you learn the guard is an example of what lyrium does to the brain.
Later on, when choosing a champion to fight for you in a Trial by Combat, you can try to choose your dog. Arl Eamon is quick to point out that the dog's loyalty could be bought with a ham bone.
In Paper Mario, an Anti-Guy guards a chest with a very useful badge in Chapter 4. You could try to tough it out and beat him in a straight fight, or you could just bring him some Lemon Candy in exchange for the badge.
To make friends with the Apple Kid in Earthbound, you have to give him a food item.
Maybe it counts more as "bait" than a "bribe", but ever since Honey was introduced as an item in Pokémon in Gen IV, it can be used to attract Pokémon. In Gen VI, it can even be used to attract Pokémon Hordes.
In Dominic Deegan, Oracle for Hire, Garrit demonstrates why the testimony of talking animals isn't admissible in court by bribing Spark to change his story about Bumper in one story arc.
Spark: I saw nothing. Bumper sucks. Gimme fish.
In General Protection Fault, Trudy Trueheart obtained a stockpile of advanced alien weapons by bribing an Alien Overlord... with cheese. Apparently, Earth is the only place in the galaxy where cheese is made, and their attempts to synthesize it (see: cattle mutilations) have so far failed.
Scooby-Doo: Perhaps the Trope Codifier. Scooby Snacks have been used in nearly all incarnations of the show to motivate Shaggy and Scooby into going into some creepy places. Parodied in Futurama, where Bender retracts his limbs and head into his body. Leela tries to coax him out with a beer. "Would you do it for a Bender-snack?"
On South Park, when those evil Canadians came to take Ike back from the Broflovskis after rescinding the adoption he refused to get in their car, until they offered him chocolate.
Jackie Chan Adventures this apparently partiallynote The fact that he was almost killed when his old boss, Valmont, ordered him to fight Shendu had something to do with it, too precipitated Tohru's Heel-Face Turn.
It's actually based on a Brick Joke two episodes earlier. Jackie tries to convince Tohru that working at Section 13 would be better and states that every Tuesday is Donut Day. He then repeats this statement when confronted with the Chans.
A few episodes of Clifford the Big Red Dog showed that Mac refused to listen to what Jetta wanted him to do, unless he was offered a Tummy Yummy as motivation.
In the episode "Honor Thy Ed", Kevin says he will give Eddy a jawbreaker if he and his friends go in the abandoned house. However, Kevin backs out of the promise a few minutes later and sucks on it after the kids see Ed fake being strangled.
In "Three Squares And An Ed", Eddy implies that Jonny would do anything for granola, in this case, dressing up like a leprechaun to distract Jimmy, who was guarding a grounded Ed.
Used a couple times in My Little Pony: Friendship Is Magic. Twilight is faced with this several times throughout "Ticket Master" by her friends in attempts to gain an extra ticket to the Grand Galloping Gala, but Twilight manages to turn away the bribes each time despite stating several times how hungry she is. Pinkie Pie also uses this against Spike in "Party of One" as part of her Perp Sweating sequence.
In Smurfette's origin episode in The Smurfs, Smurfette tempted Greedy with a scrumptious smurfberry cake into opening the village dam gate so she could flood the village back before she was changed into a real Smurf.
Kim Possible: The closing scene of "Emotion Sickness" shows Drakken frantically running and dodging plasma blasts from a Moodulator-enraged Shego. He tries yelling various apologies and pleas to calm her down, concluding with "I'll cook you dinner!"
Fancy Dinners have long been a way to smooth the waters of diplomacy. In fact in the British Diplomatic service it used to be a requirement to have a high tolerance for liquor. At times expensive food or drink was used as a bribe. A wine bottle might save face for instance when money is insulting. After all the spy you want might be a traitor but he wants to be known as a cultured traitor.
Cory Montieth mentioned that the choreographer for Glee uses candy as a bribe so that they can keep working.
Napoleon supposedly once faced an enemy army that was ill-supplied. He promised them food if they joined his army. It worked!
Animal trainers are fond of using this trope.
Bonobos (a type ape related to the chimpanzee) have been observed exchanging food for sex.