A theory

Sid from Toy Story, Master Hand, and the dad in the LEGO Movie are the same person. This timeline starts with Super Smash Bros, where Sid gets some Nintendo figures and makes them fight each other. He imagines the world of Super Smash Bros and he fills in the role of Master Hand. He imagines the toys fighting each other so he bashes and smashes the toys, breaking them in the process. This is seen in Toy Story, where years of smashing his toys together has made him almost downright sadistic with them (in Toy Story he blows up some army guys with firecrackers). Later in Toy Story, he sees the toys speak to him, and he is so visibly freaked out by this that he develops a bit of a power complex over them, making it his goal to keep toys in order. Enter the Lego Movie, where

MASSIVE SPOILER ALERT
the world of the movie is being imagined by a kid playing with toys. Not his toys but his father's toys, LEGOs. His father is downright obsessive over them, gluing them together to keep them in place and not letting his son play with them. The dad is a grown up version of Sid. He was so affected by Woody talking to him in Toy Story that he obsesses over toys and having power over them. Eventually though, he moves on from what the toys did, when he sees how his gluing and obsessiveness over the LEGOs is affecting his son. He lets his son play with the LEGOs after seeing the world imagined by his kid and how much of a jerk the bad guy is. So, all in all 3 different worlds have been created in one man's quest learning basically how to play.

TL;DR the LEGO Movie's dad, Sid from Toy Story and the implied kid in Smash Bros are the same person