The Adventures of Andre and Wally B. — Created back when Pixar was just Lucasfilm's computer graphics division (making it arguable whether it really counts as a Pixar short), this short is about a guy named Andre who tries to trick an annoying bee, and gets stung for it.
Luxo, Jr. — A Luxo lamp watches its child (the eponymous Luxo, Jr.) play with a little inflatable ball. The ball deflates, leaving the little lamp dejected, but he later returns with a giant beach ball. It was later played before Toy Story 2. And now you know where Pixar's famous Vanity Plate comes from!
This was followed by a series of even shorter shorts created for Sesame Street featuring the same two lamps.
Red's Dream — A unicycle in a bike shop dreams about being the star of a circus act, only to wake up and feel just a little bit more depressed.
Tin Toy — A toy tries to escape a terrifying baby. It's no coincidence that it has the same "toys are alive" concept as Toy Story, as it led to the creation of that film. It was also the first computer animated film to win an Academy Award for Best Animated Short Film.
Knick Knack — A plastic snowman in a souvenir snowglobe tries to escape. It was later played before Finding Nemo.
After Pixar made it big in feature films, they returned to making theatrical shorts, which played in front of most of their animated films (except for Toy Story 2 and Finding Nemo, which used old Pixar shorts instead):
For the Birds (played before Monsters Inc) — A bunch of little birds try to drive away a fairly harmless big bird from their perch on a telephone wire, only for their efforts to backfire in their faces.
Boundin' (played before The Incredibles) — A rhyming, musical short (as opposed to the many dialogue-less shorts before it) about a former show-off of a sheep who learns how to cheer up after having his beautiful wool shorn off and being embarrassed in front of his friends.
One Man Band (played before Cars) — Two street musicians compete for a little girl's tip, only for the girl to teach them a harsh lesson about being too competitive.
Lifted (played before Ratatouille) - Your average driving test, only with alien abduction instead of driving.
Presto (played before WALL•E) — A magician's hungry rabbit hilariously torments its owner over a carrot.
Partly Cloudy (played before Up) — A cloud produces baby rams, baby crocodiles, and other dangerous babies, much to his Delivery Stork's... misfortune.
Day & Night (played before Toy Story 3) — A traditional animated short, but with 3D elements, about two characters named Day and Night, who are the Anthropomorphic Personifications of daytime and nighttime (respectively).
La Luna - Originally hitting the festival circuit but eventually played before Brave; a young boy is taken out to sea one night for the first time by his papa and grandpa, to learn about their unusual line of work. They sweep the moon clean of fallen stars!
The Blue Umbrella - Presumably set to show before Monsters University, tells the story of a blue umbrella falling in love with a red umbrella.
Some of Pixar's features have a bonus short on their DVDs depicting the further adventures of the characters in the movie:
Mike's New Car (follow-up to Monsters Inc) — Mike buys a new car, but he and Sulley can't quite figure out how to work it...
Exploring the Reef (related to Finding Nemo) — Jean-Michel Cousteau tries to make a documentary film about coral reefs, but Marlin, Dory, and Nemo keep interrupting him. Eventually, things are learned about corals, but Cousteau still feels "upstaged".
Jack-Jack Attack (follow-up to The Incredibles) — During the events of the movie (while Bob, Helen, Violet, and Dash are on Syndrome's island, to be precise), Kari the babysitter has her hands full with Jack-Jack, who's just discovering his numerous (and deadly) superpowers.
Mater and the Ghostlight (follow-up to Cars) — After the sheriff of Radiator Springs tells a spooky story about "the ghostlight", Mater becomes scared of running into it.
Your Friend the Rat (follow-up to Ratatouille) — Remy and Emile educate viewers on the history of rats and their relationships with humans, hoping to create a better understanding between the two species.
BURN-E (follow-up to WALL•E) — A short depicting just what happened to the robot that accidentally got locked out of the Axiom after WALL•E and EVE's flight around the ship who is continually trying (and failing) to repair a light.
Dug's Special Mission (follow-up to Up) — A short film that tells what Dug the dog was doing before he meets Carl and Russell in the film. As hinted at in the feature, Alpha (with Beta and Gamma) send Dug out on a "very special mission" to retrieve the bird. They only intended for it to distract him and keep him from causing trouble or bothering them while they hunt, but as we see in the film, he actually does find the bird (Kevin).
George and AJ (another follow-up to Up) — Carl's stunt inspires, one week later, many other old people to do the same with various ways... To George's and AJ's (the two Shady Oaks orderlies) despair (And our enjoyment).
Additionally, a series of shorts following up Cars called Mater's Tall Tales was produced for the Disney Channel:
Rescue Squad Mater — Mater tells a story about how he was a firetruck. Oh, and he was a doctor too.
Mater The Greater — Mater claims to have been an Evel-Knievel-style daredevil in a previous life.
El Materdor — Mater is now a bullfighter. The bulls in question are bulldozers.
Tokyo Mater (played before Bolt) — The first Pixar short to play before a non-Pixar film, and their first theatrical short to be based on a previous movie, Tokyo Mater centers around a story Mater tells about him getting involved in a drift race in Tokyo.
Unidentified Flying Mater — Mater makes friends with a small flying saucer spaceship that speaks in a strange robotic voice. The UFM (called "Mator") teaches Mater how to fly, but gets taken away to Parking Area 51.
Heavy Metal Mater — During a night of karaoke at Flo's, Mater recounts how he used to be a big rock star in a heavy metal band.
Moon Mater — Mater is inducted into the NASCA space program. His mission: Rescue Impala XIII, who has broken down on the moon.
Mater Private Eye — Private investigator Mater must solve a case about counterfeit tyres and track down the whereabouts of Tia's sister, Mia, who's been car-napped.
Air Mater — Mater goes to a town inhabited by planes and learns to fly. It was released on the Cars 2 DVD and acts as a set up for the upcoming Spin-Off film Planes.
Time Travel Mater — Mater accidentally travels back in time to when Stanley first discovered the original Radiator Springs and with Lightning, ensures that history remains on course. Premiered at Disney California Adventure and features locations introduced in the Cars Land expansion of the park where Stanley set up the beginnings of the town as a rest stop for traveling cars.
The Toy Story trilogy has follow-ups in the form of Toy Story Toons:
Hawaiian Vacation (played before Cars 2) — Barbie and Ken end up in Bonnie's bedroom after a failed attempt to stow away on her trip to Hawaii, so the toys all try to create their own island paradise.
Small Fry (played before The Muppets) — The first Pixar short to play before a live-action movie, Buzz gets left behind at a fast food restaurant and encounters lost kids' meal toys.
Partysaurus Rex (played before Finding Nemo 3D) — When Rex finds himself left behind in the bathroom, he puts his limbs to use by getting a bath going for a bunch of new toy friends.
A series of "Toy Story Treats" (and similar bumpers with Sarge and his soldiers) were also made and shown at commercial breaks during the Saturday morning cartoon block on ABC (for the last season before One Saturday Morning debuted). The shorts have since been included as easter eggs in the various DVD/Blu-Ray releases of the Toy Story movies (though the bumpers weren't).
These shorts contain examples of:
3-D Movie: Tokyo Mater, Partly Cloudy, Day & Night, and Knick Knack have all been rendered in stereographic 3D.
It's worth mentioning that the original 3D version of Knick Knack (with weapons-grade boobs) got shown at SIGGRAPH.
An Aesop: Day & Night has one about how "different" doesn't necessarily mean "bad."
Amusing Injuries: Pretty much everything the magician goes through in Presto, as well as Mike's injuries after getting locked in the engine of his car in Mike's New Car. In Partly Cloudy the stork suffers various injuries from the animals it must deliver. In George and AJ, it's the ambulance who keeps being "hurt" over and over (gets knocked over three times, gets an oxygen bottle on it, and is crushed by Muntz's-now-Carl's zeppelin!)
Chekhov's Gun: This was the impetus for the "Mater's Tall Tales" shorts, as a key aspect of Cars 2 is Mater's fanciful storytelling. Since this was a trait not shown in the first film, the Pixar staff feared that its sudden appearance would look like an Ass Pull. The "Tall Tales" shorts averts the problem by establishing this trait ahead of the movie.
Continuity Snarl: Dug's Special Mission features Alpha talking in his high-pitched voice, in scenes set before the other dogs are surprised by it in the film.
Did You Die?: In the short "Mater the Greater", when Mater claims that it was Lightning McQueen who tried performing a death-defying leap across a canyon...and that he "didn't make it". It's Lightning himself he's telling the story to.
Educational Short: Arguably, Your Friend the Rat both spoofs this and plays it straight.
Executive Meddling: Subverted. It's assumed that the decrease of the women's bust size in Knick-Knack is Disney executive censorship as usual, but John Lasseter and the studio actually made the decision to do so themselves.
Parodied in Your Friend the Rat, which ends with a prolonged legalistic crawl warning people that Pixar does not encourage people to have contact with rats. Remy and Emil bitch about the inclusion of this producer-imposed warning (which is Comically Missing the Point of their presentation) and even push the crawling words aside as best they can.
Hammer Space: Mike's New Car, considering Sully could lower the passenger seat to the point only his head is visible.
Herr Doktor: In "UFM: Unidentified Flying Mater", the Parking Lot 51 scientist pitties, as well as "Dr. Aschleppwagen", Mater's disguise, when he uses to try and save Mator. A real scientist pitty sees Mater.
German car: So, herr doktor, what does "dad gum" mean? Mater: (fake German accent) Ze "dad gum" means... (drops accent, saves Mator) ...let's get outta here!
Meaningful Name: The two musicians in One Man Band are named Bass and Treble (after the two music clefs in common use, ignoring the less common alto and tenor), and the little girl they both want a tip from is named (Drum Roll Please)...Tippy.
Medium Blending: The title characters of Day & Night are traditionally animated, yet the imagery inside them is done in CGI.
Your Friend The Rat combines CG for the scenes with Remy and Emile, stylized traditional animation for most of the other scenes, live-action Stock Footage, and a brief Stop Motion shot.
No Antagonist: In contrast to Pixar's feature length films, quite a few of the shorts use this trope.
Oh Crap: The first bird to realize what was about to happen in For The Birds. Also, Stu (the alien student in Lifted) when he accidentally releases the tractor beam on Ernie (the farmer). George and AJ keep having it over and over again.
In Exploring the Reef, whenever Jean-Michel Cousteau says his name, a fanfare Leitmotif plays, making the fishes look around for the source of it.
Shades of Conflict: White vs. white, white vs. gray and gray vs. gray depending on the short, with Geri's Game even going so far as to have the both opposing characters apparently be the same person. Not counting the ones based on Pixar's feature-length films that have a villain from the film appear (Jack-Jack Attack, Dug's Special Mission), the only Pixar short with clear-cut villains is Lifted (and even that's a matter of some debate).
Near the end of BURN-E, there's a reference to a very famous scene from 2001: A Space Odyssey.
One of the discarded kid's meal toys in Toy Story Tunes: Small Fry was based on Condormannote On top of the obvious Disney shout out, there's a probably unintentional twist here in that this live-action hero was played by Michael Crawford — whose work in Hello, Dolly! proves so important in WALL•E!.
WALL•E is driving a lunar exploration vehicle in the ending scene of Your Friend the Rat.
Time Travel Mater is an homage to Back to the Future, including a scene where Mater fears Lizzie might fall for Lightning and alter the time stream.
In Partysaurus Rex, when the bath toys are lamenting how they can't play after bath time due to a lack of arms, one toy cries out in anguish, "No more tears!".
In the same short, the fuzzy toilet seat cover is Sully's fur.
However, it's revealed at the end of each short that Mater's story actually did happen. Guess which story was completely made up!
Guido: Modify! (he puts several wooden boxes on Mater's body, with the last one forming his missing "hood")
Mater: Hey, look! I'm "motterfied!" (he starts making fake motor sounds while scraping the boxes on the body across the pavement, sending sparks flying into the air. McQueen palms his windshield with one of his front wheels)
Also, in Cars 2, Kabuto can be seen with his modifications again.