In Toy Story 2, when Mr. Potato Head and Rex arrive at Tri-County International Airport, an announcer says: "The white zone is for immediate loading and unloading of passengers only. No parking." When Mr. Potato Head parks the Pizza Planet Truck right outside the terminal (just as Ted Striker did the taxi he had commandeered at the start of Airplane!), Rex thus complains, "We can't park here, it's a white zone!"
In WALL•E, the autopilot is called AUTO, a nod to the Airplane! autopilot (a blow-up doll called Otto).
One of the pilots in Airplane! is called Rex (Kramer).
Toy Story 3 is the only Toy Story movie that does not parody Airplane!.