Mischief-Making Monkey

Monkeys are often portrayed in fiction as mischievous little pranksters, who like to steal things (Hats seem to be a common target), throw stuff at people, and otherwise make monkey business.

Examples of Mischief-Making Monkey include:

Anime and Manga

In Inuyasha, three little monkey youkai appears as playful pests. Subverted by their leader Sarugami, who's The Stoic.

Film

In Rio, the macaques are all thieves and con artists (within the animal kingdom, at least).
Abu from Aladdin is a thief. And not a thief like Aladdin is a thief, who steals only what he really needs to steal. Abu steals anything and takes great pleasure in using it to mess with people.
In the Charlie Chaplin film The Circus, one scene featured The Tramp performing a tightrope routine because the regular could not be found. While highly entertaining, especially after The Tramp's safety harness falls off, a group of monkeys that has harassed Chaplin's character throughout the movie decides to get involved, crawling all over him, biting him, and removing his pants.

Live Action TV

On an episode of The Lucy Show, Lucy gets a job babysitting, but finds out she's expected to care for a couple's three chimpanzees which they see as their children. The chimps put off going to bed with all sorts of tricks including riding bikes and playing Cowboys and Indians. The couple comes home to an exhausted Lucy who apologizes that the chimps aren't in bed. The "parents" are just glad she didn't run away like the last babysitter.
In Friends season one, Ross had a capuchin monkey named Marcel in order to get used to having someone who depended on him, in preparation for his then-unborn son. It got into a lot of mischief, including setting the girls' TV to the Spanish language SAP. Ross eventually gave it to a zoo, and it was last seen (I think) starring opposite Jean-Claude Van Damme in Outbreak 2.
Community: Annie's Boobs, the thieving monkey.
On How I Met Your Mother Marshall may or may not have been mugged by a monkey; he refuses to say. From the same episode, Ted claims a monkey stole a doll, climbed a model of the Empire State Building and was attacked by paper airplanes, but fans have their doubts.

Literature

Sun Wukong from Journey to the West is what happens when a mischievous monkey gains extreme god-like powers. Had it not been for The Buddha's intervention, he would have overthrown heaven.

Video Games

Scarab of Ra has a monkey that cannot hurt you, but likes to steal your gold and whatever else you might be carrying. Then after it's robbed you bare, it might come back to tweak your nose.
Kingdom of Loathing has a kleptomaniac monkey familiar that increases meat drops when used (meat being Loathing's currency, in a bizarre justification of the Money Spider trope).
In Samurai Warriors, Toyotomi Hideyoshi has a monkey motifs and has a mischievous, playful attitude.
In Yoshi's Island, the third world is mainly inhabited by monkeys called Grinders that spit watermelon seeds at Yoshi and sometimes drop bombs.
Super Mario 64 had the hat-stealing Ukiki of Tall, Tall Mountain.
In The Lion King, the second level had a lot of monkeys hanging from trees waiting to toss something around. That something is Simba, who can roar at them to change the direction they toss him.
The Chimp from Super Mario Galaxy 2 is a blue chimpanzee that will challenge Mario/Luigi to some sort of challenge several times in the game, such as stomping as many Goombas as possible, ice skating to knock out enemies a la Whack-A-Mole, bowling over pin-shaped enemies using the rock power-up or swimming for coins.
Aipom and Ambipom from Pokémon fit this description to a tee. Mankey as well, provided that it isn't angry at something.

Western Animation

Rhinokey from The Wuzzles, although he's only half monkey, is the joker of the gang.
Master Monkey on the TV series Kung Fu Panda is the most mischievous of the Furious Five, although it is not seen often in the movies.
Mr. Twitchy from Rated A for Awesome hinders the gang just as much as he helps them.