Are all Pixar movies set in the same universe?

Possibly, but it doesn’t seem to be by design.

A Pixar employee, Jay Ward, who was fairly involved in Cars, was asked about this shortly after the posting of Negroni’s theory in an interview with Jason Torchinsky at io9. He rebuts the theory:

JT: What do you think about it?

JW: I think somebody had a lot of time on their hands. They may have had some other recreational activities…

JT: So would you go as far as to deny that there's a common thread —

JW: It's almost like the 9/11 conspiracy theories… it’s like, really? No, the movies were sort of made in a different order by different directors in different times, in different places. It's cool that it all worked out that way, but it probably was not intentional.

— Pixar’s Jay Ward responds to the unified Pixar movie theory

He’s the only Pixar employee I’ve ever seen discussing the theory, so unless another answerer can find somebody different, I’m inclined to say that it really is just a theory.

As a side note, Cracked and Negroni were by no means the first people to propose the idea of a shared universe (although Negroni might be the most detailed suggestion). There’s a Wikipedia article for the Pixar Theory, which says “Media discussion about a “Pixar Universe” has existed since at least 2003”.

(This is copied from my answer to Is there any official evidence for the Pixar theory on the Science-Fiction and Fantasy Stack Exchange.)