Both the Alien Slime soda dispenser and the Whack-a-Alien game at Pizza Planet are a reference to the titular monster from the film series Alien.
When Buzz (excuse me, "Mrs. Nesbitt") is having tea, he says he's "sucking down darjeeling with Marie Antoinette and her little sister." The dolls are both headless, so which is which doesn't matter so much, but this is (potentially) referencing both Marie Antoinette's fate of beheading and Wednesday Addams's doll. Also, they're taking tea from a Utah teapot.
The way Woody communicates through his speaker box without the string being pulled, and not moving (at the beginning of the backyard scene) is reminiscent of Talky Tina.
In the chase scene at the end, you get a quick glance inside the car, and the radio's playing Hakuna Matata.
Towards the beginning, a shark toy pops out of the toybox wearing Woody's hat and says "Look! I'm Woody! Howdy howdy howdy!". A very similar joke - involving a vulture in a cowboy hat - appeared in The Far Side.
When Buzz is running away from the giant globe, the sound effect of the globe rolling is pulled from the boulder in Raiders of the Lost Ark.
In Sid's House of Terror, the carpet in the hallway matches that of the Overlook Hotel.
When Sid is torturing Woody, he quips "We have ways of making you talk.", referencing a (misquoted) line from the film "In The Lives of a Bengal Lancer" (1935).
In the opening sequence, listen close and you'll catch at least half a dozen classic sound effects from Star Wars, including the Darth Vader breathing, the lightsaber sound, and the blaster sounds from both the X-Wing and TIE Fighter.
Pay close attention as they flip through the channels and you'll see snippets from several Pixar Shorts on the TV.
The toy repairman is Geri from the Pixar shortGeri's Game, where he plays a game of chess against himself. While he's repairing Woody the music from the short plays and one of the drawers in his toolbox is filled with chess pieces.
Rex with "Objects are closer than they appear" in the toy car's rearview mirror in Toy Story 2, to the scene DEAD ON from the T-Rex Chase in Jurassic Park, Hilarity Ensues.
Potato Head takes off his hat and throws it at the door of Al's apartment building to keep it from closing. Oddjob from Goldfinger couldn't have done it better.
Buzz comes across the new line of Buzzes in the toy store, and notes the snazzy utility belt, saying "I'd like to get me one of those," echoing Tim Allen's fixit man character in Home Improvement (who often wore a toolbelt).
Slinky-Dog says "I'm not a smart dog, but I know what roadkill is.", parodying the line "I'm not a smart man, but I know what love is." from Forrest Gump, another movie that starred Tom Hanks.
A plush Totoro toy appears as one of Bonnie's toys in Toy Story 3. (It should be noted that Pixar has done the English dub of every Miyazaki movie since Spirited Away, and Lasseter is close friends with Miyazaki himself.)
Miyazaki is referenced even in the credits with a "special thanks".
Right before the preschool kids burst into the room, some smaller toys are hiding and quivering under a cabinet, mirroring Tin Toy
Many people have made note of the similarity between Big Baby and the terrifying, doll-like baby in "Tin Toy". They even make the exact same sounds!
One of the daycare kids looks just like an older Boo from Monsters, Inc.. The first time we see her, she's playing with a blue cat and a sunflower, and says "Boo! No no no! What's the matter?" She's reenacting the scene from Monsters, Inc. where Sulley accidentally scared her.