Pixar decided that it wanted G.I. Joe to be one of the toys in the movie but, when Hasbro refused to licence the rights to the action figure, Mr. Potato Head was added to the cast instead (along with the fictitious "Combat Carls").
Disney was sued by New Jersey company Diece-Lisa Industries in 2014 over Toy Story 3's evil "Lots-O'-Huggin'" toy (better known as Lotso), alleging that they had been selling their own "Lots of Hugs" toy bears since 1995.
Joss Whedon, who was brought on to do a script revision for Toy Story, wanted to include a kickass Sarah Connor-esque Barbie character in the first movie, but Mattel refused to licence the doll to Pixar, fearing the movie would be a flop. They apparently changed their minds, as Barbie later appears in the movie's sequels.