Understand that this page contains [mostly] user-submitted, non-verified content. Hence it barely contains all references that exist, but only a mere fraction. If you've spotted a reference, feel free to add it down below with a compatible description. Add links if needed.
There's an NPC by the name of Lun-Chi located in Kun-Lai Summit, near the Temple of the White Tiger. Under his name appears the title, <The Streetfighter>. This would appear to be a reference to the character Chun-Li, from the Street Fighter game series.
A quest called Unsafe Passage given by Koro Mistweaver in Krasarang Wilds results in a part of dialog from the game Skyrim, where the guards would repeatedly say "I used to be an adventurer like you, then I took an arrow in the knee", which also became an internet meme later on. In the quest, while escorting Koro Mistweaver, you are attacked by a group of Riverblades, after which Koro would say: "Help me up, <name>. I... I took an arrow in the knee...".
An NPC located in The Jade Forest by the name of Dook Ookem is an obvious reference to the main character of the video game series, Duke Nukem. His quotes are also said to be based on the character.
There's a house on top of a mountain in The Jade Forest, which has a reasonable amount of balloons connected to it. Inside the house, is a pandaren named Kar (which would be a reference to the old man in the movie, named Carl). Outside the house is a single grummle by the name of Rusty Nail, carrying a backpack, accompanied by a fox named Dig - these would be referring to the young boy by the name of Russell, and the dog, named Dog.
The achievement How To Strain Your Dragon would appear to be a word play of the said movie, How To Train Your Dragon, in which there's a dragon race at the end of the film.
The achievement Number Five Is Alive is a reference to Number 5, a designation given to 1 of 6 robots in the movie "Short Circuit". After being struck by lightning, "Number Five" becomes convinced that he is alive, and not just a machine. The achievement itself is the declaration made by the robot: "Number 5, not a machine. Number 5..... Is alive!"
There's an NPC named Adele located in Townlong Steppes, more specifically in an area named The Widening Deep. The NPC moves by rolling on the ground, and with the name of the location, this is an obvious reference to the singer Adele and her song "Rolling in the Deep".
The achievement Every Day I'm Pand-a-ren is an obvious reference to the song "Party Rock Anthem" by LMFAO, in which the phrase "every day I'm shuffling" is presented with a similar syllabication.
The male pandaren /dance animation is based off of the choreography from LMFAO's music video, "Party Rock Anthem".
The daily quest Red Blossom Leeks, You Make the Croc-in' World Go Down is a play off the lyrics from the song "Fat Bottomed Girls", where the actual phrase would be; "fat bottomed girls, you make the rockin' world go round".
The scenario Assault the Shipyard for the Isle of Thunder achievement has a sub-quest named after the Mega Man rock-opera bands songs, notably Light up the Night, and Breaking Out
There's an area named Honeydew Village located in The Jade Forest. This could be referring to Simon (better known as Honeydew), a member of the YouTube Let's Play group, Yogscast. Yogscast is an internet sensation that has promoted World of Warcraft in many ways, and therefore it would only make sense for this to be a dedication to Simon and the entire Yogscast team.
The achievement What Does This Button Do? is a likely reference to Dexter's sister Dee Dee who would often say, "oooooooooooo, what does this button do?" before pressing buttons at random on various machines in his lab.
The Singing Pools, an area which is located in the pandaren starting area, The Wandering Isle, could be a vague reference to the Japanese manga series, Ranma ½, as if you fall into any of the pools, you're transformed into an animal.
There's an NPC located in The Jade Forest, by the name of Kher Shan, which is a reference to a character by the name of Shere Khan from The Jungle Book stories.
There's an NPC by the name of Lon'li Guju in Kun-Lai Summit. This NPC is referring to the last Pinta Island tortoise, who became world-famous but passed away on June 24, 2012. If a player emotes something such as /wave or /love at the tortoise, he'd start to follow the player for a while.
Cornan <The Barley Barbarian>, an NPC in Valley of the Four Winds appears to be a reference of Conan the Barbarian, a fictional sword and sorcery hero that has been included in many different sorts of media (games, movies, comic books etc.)