Here’s my theory:
The way I see it, Toy Story and Monsters Inc. take place together. They just seem like two movie series that fit nicely with one another. Also, I can see Finding Nemo (the Buzz in the waiting room), Up (the Carl-and-Ellie Postcard in TS3), Ratatouille (if Finding Nemo can have sentient fish and birds and Up can have sentient dogs, then there’s no reason I can see regarding Ratatouille also taking place along side them), and maybe WALL-E (the Rex in WALL-E’s truck and the BNL batteries in TS3) in there as well.
The Incredibles could be a film-within-a-film (since it doesn’t really fit with the others and there’s a Mr. Incredible comic book in the Dentist’s office in Finding Nemo). The Cars Franchise, I’d like to think, is sort of like the intro to Toy Story 3, in that it takes place inside a kid’s imagination while playing with toys. A Bug’s Life is somewhat tricky. In TS2, there are a ton of Bugs Life background references (Andy’s calendar, the book Mrs. Potato Head is reading, the toys at Al’s Toy Barn). So for me, it’s either that it takes place in a child’s imagination or it’s a film-within-a-film sort of thing.
Or they all just take place in their own separate worlds and not everything is connected.
CaptainJZH - Just checking; are you aware of the comic crossover between Monsters,Inc. and Toy Story?
Yes. I haven’t read it, but I know of it.
I think it’s a cool theory!
I think there could be a connection between a couple of the different movies (For example, Ratatoullie, Up and Toy Story), but some of them just take it a little too far. 
I don’t know.
Guys, we are having a bigger problem all over the Internet. It’s like several other individual theories related to Pixar films are constantly continuing to be made up by deluded fans–which makes me mad because every time I go on a rant trying to explain that none of them are true, all I get from them is a bunch of lame excuses, such as “You just don’t get it.” and “It’s just for fun.” and a whole bunch of repeated questions that say the same details as the theory itself from which I have to constantly answer with the same set of my disproval statements over and over again. 
This has happened on both my Twitter and YouTube accounts, mostly. And if those fans are refusing to believe me every time I try to tell them, it’s because they are being deluded away from the true brightness and color of the actual films themselves, and I have reason to believe that everything being said within the entire theory itself is obviously just being used as a lame excuse to prevent newbies of the fandom from watching the actual films themselves, by luring them to the untrue and dark-sounding details instead–all of which has gone too far widespread ever since that blogger Jon Negroni started it and therefore that’s why it must be stopped, 'cause I am really afraid (and worried) that the theory is a threat to both the studio’s future and its entire fanbase.
When are people going to realize that Boo does NOT time-travel through doors in search of Sulley and become a witch?! Or that Jessie’s previous owner does NOT become Andy’s mom?! Or that the Axiom has NOTHING to do with Cars?!
But other than that, I’ve noticed a huge number of other theories appearing recently. First, someone had suggested that Carl was dead with Russell being his guardian angel. Then someone else suggested that Edna Mode was once previously associated with Syndrome. None of these are true, either. The WORST part was that, last winter, when I recieved one of my e-mails from Topical Digest, I got really MAD because SOMEONE had called WALL-E a “villain”! And not only that, but at the same time it looked like whoever was saying that had obviosuly altered his cute, sad-looking googly eyes into mean-looking ones! THAT one right there, I really HATED the most.
All of this, right there, is further proof that fan theories–especially the ones related to Pixar films–have somehow already become a huge problem across the Internet, especially in recent months. And I think it’s time we, the true fans who know exactly what is wrong with the theory and its many noticeable flaws, try to do something about it. (Does anyone else agree?)**
–evspixarfan2012
We don’t need to. The Pixar theory, as well as all other Pixar shared universe theories, are long dead as confirmed in this one interview with the directors of Inside Out:
youtube.com/watch?v=h74nAbx9Fgw
So there you go, indisputable disproving of that wretched fan theory. Of course seeing as that video has literally a 1000th or so the views one of SuperCarlinBrothers’s ongoing videos about how this recent Pixar film or that recent Pixar film fits into the theory does, it seems like we know how much the internet cares.