In Toy Story 1, the main antagonist is Andy's' neighbor "Sid".
After a series of events Buzz and Woody end up in Sids' house, and this is bad because Sid "tortures" his toys.
Now Sid doesn't know the toys are alive and can "feel" the pain so it really isn't his fault. In the end of the movie it is revealed to him that the toys are in fact alive which ends up traumatizing him.
15 Years later (Toy Story 3) Sid returns as the garbage man.
Now the conspiracy is about WHY Sid became a garbage man. Some would say it's because he became a "loser" and couldn't get a better job. According to a Reddit user, Sid became a garbage man to protect toys that are getting thrown away by people who don't know the toys are alive. Working as a garbage man helps him find these abandoned and broken toys. Allowing him to take them home, clean and fix them up; and donate these toys to children who want them. This conspiracy theory does work because it could also be a way of Sid trying to make up for all the wrong he did to his past toys.
Link to the Theory: http://www.reddit.com/r/FanTheories/comments/2l42t5/toy_story_3_sid_became_a_garbageman_to_do_one/
For the readers who are unfamiliar with the premise of the show, it's about a lab mice called the Brain that constantly tries to develop plans to take over the world. The Brain would come extremely close to his world domination plans succeeding but Pinky, the "insane one" ends up ruining the plan at the last moment.
Pinky is on the left and the Brain is on the right
On first impression, people assume that in the show "Pinky and the Brain", Pinky is the idiot while the Brain is the smart one. However, this particular conspiracy theory challenges that notion by suggesting the opposite; that Pinky is the smart one while the Brain is the idiot!
The first piece of evidence that points to this is that in the song's opening theme, the lyrics state "one is a genius, the other insane". However, the lyrics themselves never explicitly state which of the two mice is a genius.
Of course this alone isn't enough evidence, but it was enough to get devoted viewers of the show to look for more possibilities pointing to Pinky as the genius. Turns out there was more evidence!
Another of the premise within the show is that Pinky would always bring up an excellent counterpoint to the Brain's plan which the Brain would always ignore because he thinks that Pinky is an idiot. Ironically, Pinky ends up being right by the end of the episode and the Brain's plan is thwarted.
Furthermore, some episodes shows Pinky being engaged reading a book, indicating that Pinky is interested in learning. On the contrary, an episode parodying Jeopardy reveals that the Brain is actually unable to spell his name.
The evidence piece that supports this conspiracy theory the most would be in the episode "That Smarts". The Brain creates a "Smart Machine" in an attempt to make Pinky more intelligent. However, the Smart Machine changed nothing about Pinky which indicates two possible outcomes. The first outcome is that Pinky is already a genius that can't be improved further, the second outcome is that the Brain is an idiot because he is unable to design a machine that works properly.
For further information regarding this conspiracy theory, I've found this website and youtube video helpful.
