Wyldstyle's introduction, feats of skill, and role in rescuing the prophesied hero is comparable to that of Trinity of The Matrix. The Think Tank is similar in concept to the cells where the Machines put the humans to use them as living batteries. There's also Emmet finally grasping the rules of his universe in the climax.
BIONICLE, LEGO Speed Racer, Fabuland and LEGO Friends get a reference in a blink-and-you'll-miss-it montage explained by Wyldstyle. The map of the LEGO universe can be seen in another part of Wyldstyle's Expospeak, containing further references to LEGO themes, such as Atlantis, Pharaoh's Quest, Technic Mecha Cave and Vladek's Realm.
At Cloud Cuckooland, Batman is annoyed by a clown and a man in a dino suit. So the Joker and Killer Croc, essentially. Alternatively, the dino suit could be a reference to the T. rex Batman keeps in his Batcave.
Emmet's fall down the black hole marking the edge of the universe resembles the Stargate sequence from 2001: A Space Odyssey. Additionally, Lord Business refers to his flying headquarters as a "black monolith".
An extremely subtle reference is slipped in during the climax, shouting out to BrickFilm community. One of the first major BrickFilms (stop-motion movies made out of Lego, no doubt a big inspiration for the film) was ''The Magic Portal'', made sometime in the late 80s. Now, look at the tube that Finn uses to send Emmet back into the Lego world at the end: what's it called? The Magic Portal.
Batman crashing the Batwing through the "sun" and producing a Bat-symbol is likely a Shout-Out to the 1989 Batman film, wherein the plane did the same thing to the Moon. The symbol itself is the one used in The Dark Knight Trilogy.
When chasing Wyldstyle and Emmet in the city, Bad Cop says on his radio: "Release the Copper-Chopper!"
Lord Business later declares: "Release the Kragle!"
When Metalbeard states the rules of piracy, one of the rules that can be seen is: "Never release a Kraken."
Lord and Miller love to reference their previous work, Clone High:
A dolphin chirp is thrown in when Emmet is being booed by the Master Builders (specifically, from a shark that someone threw at him). Dolphins were a Running Gag in Clone High.
The Cleopatra mini-fig waves pom poms when the NBA all-stars are fighting Bad Cop and the micromanagers. Cleo in Clone High was a cheerleader.
The DVD-exclusive short Michelangelo and Lincoln: History Cops has definite shades of Black and Tan from the episode "Film Fest: Tears of a Clone".
The term "Master Builder" is a title given to employees of LEGO whose job entails helping to design new sets and also building large, complex statues out of LEGO bricks, the kind that are commonly displayed at LEGO theme parks and retail stores.
When Wyldstyle yells "I found your pants, series is over!", it seems like a reference to How I Met Your Mother, a series that ends when the title of the show is answered. Specifically, because directors Lord and Miller wrote for that show.
When the team infiltrates Lord Business' Tower, Wyldstyle tells Emmet that they're in the clear by giving him The Signal