The Brave Little Toaster/WMG

Rob secretly knows that the appliances are alive.
Ever wondered why he's such a pack rat? Not because he's very frugal, but because he knows of their sentience. The appliances, however do not know that he does; Rob knows because he accidentally saw them moving, unknowingly to them. When he came back to his house, found the group missing, and acted puzzled, he was playing stupid. Finally, the reason Rob is laughing his head off at the end? To cover up the laughing of his "friends" in the trunk!

Syndrome from The Incredibles survived and grew up to be Elmo St. Peter.
The hair... the gadgets... the cruelty...
 * Or maybe it was Dexter, who shed his accent to fit in, and is trying to rebuild his life after an experiment destroyed all of that ground-breaking technology in his basement.

The movie is a Christian allegory dealing with Christ's second coming.
Just think about it: five appliances wait patiently for their MASTER to return (God/Jesus is sometimes called our Master). They are almost tricked into thinking that he has abandoned them, but they overcome this and set off to find him and the CITY OF LIGHT (Heaven). Their many adventures are metaphorical for the trials and tribulations of life. No matter how many dangers they face, they NEVER LOSE HOPE that they will find him. However, in the end,
 * What about ? Does that mean He forgives and heals even those who lose faith? ...excuse me, I'm gonna go visit church.
 * = Lazarus. Master's ability to fix the appliances is another sign he is Jesus.
 * Elmo St. Peter is Satan, his dog Quadroped standing for Cerberus, the guard dog of Hell. All of the appliances trapped in his shop are former believers who've lost their faith. That is, until the Toaster and friends *save* them.

Alternatively, or in addition, it is partially a holocaust allegory.
The appliances are forced to leave thier home and go on a dangerous journey to find the Master, without being seen by any other humans--simmilar to Jews/Gypsies/etc having to flee their home countries and escape to America. Radio talks like a 1940s broadcaster, and makes constant references to WWII. Then there's Lampy's exclamation of "to the showers!" when he thinks he is about to be thrown away (seriously, he says that). Elmo St. Peters is essentially a Dr. Mengele to the appliances. If the appliances are caught by humans, there's the fear that they must remain useful, or be destroyed. And we probably shouldn't even get into the junkyard scene...

Lampy is the Pixar lamp, dyed orange.
Go on, tell me he ain't.

Alternately, Lampy was the inspiration for the Pixar lamp.
Given that many of the people who worked on this film went on to work with Pixar, this is very probable. Also, they are both living objects, though Lampy actually has a face and can speak.

When master read books under Lampy he was educating the lamp without realizing it.
Though slow on the uptake and not very street-smart, Lampy is still oddly smart in other ways compared to the other appliances. He knows how to read a phone book, and while the other appliances call the sun "The really big lamp in the sky," he understands meteorology well enough to know that he can make himself into a lighning rod to recharge their battery. That's because while other kids would be reading comic books or dirty magazines under their lamps, Master is exactly the type of nerd who would be eagerly reading his science textbooks. "Lampy: You know, I've been thinking, and this college business seems like a good idea. I can absorb a lot of interesting facts."
 * This is somewhat implied by the following line near the end:

Radio actually belonged to Master's parents or grandparents.
Hence why he sounds like he's from the 1940s, and his obsession with WWII. Master probably got the radio as a family gift, considering it a cool antique.

Appliances and electrical objects actually are alive!
I just had to say it. But it kind of explains exactly how they do their jobs. Please don't take this WMG too seriously.

This film, Cars, and 9 are all alternate branches off the same timeline.
As in 9, the Industrial Revolution never ended. But in this timeline, the manufacturing companies held a secret skill: They were able to make living beings...living beings disguised as household appliances. Only the manufacturers know this; everyone else does not.

Alternately, this movie is the prequel to 9
This would explain the reason the appliances come to life. The producers of said appliances used the same technology the scientist of 9 used to bring the stitchpunks to life. Thus, Toaster, Lampy, Kirby, and all the rest are not only sentient, but have souls.
 * Good lord, does this mean that the air conditioner is a past incarnation of 1?

Toaster is a regeneration of Rob, who is the inventor of the living appliances.
First of all, Rob is a Time Lord. When Rob got older, he discovered a hidden talent. So he went back in time so that he could introduce a new technology to the world earlier. However, he lost control of his powers and was sent back to the 1930's or 20's. After 20 years or so, he came up with a new type of technology. It was a sort of "heart" that would actually give sentience to appliances and other electrical objects, to better allow them to perform jobs. This secret, held only by manufacturers, was soon applied to other objects, such as vehicles. A few years after he came up with this, he passed away while driving in the country. Being a Time Lord, he regenerated, but somehow did so into a walking, talking toaster. He realized that his car had stopped very close to his old childhood home, and headed there, being followed by the car. After a few more years, he saw himself as a young kid. Not wanting to creep himself out, he invented the name "The Master" to call his future (or was it his past) self by. The other guys soon picked up this term.

Toaster saved Rob/The Master not only because he wanted to, but also to avoid creating a Grandfather Paradox.
See WMG above for details. If the human Rob would have died, this would have negated everything leading up to his time travel, invention of the living machines, and eventual death, making Toaster unexist, as well as negating all the events of the movie. This becomes a Wall Banger when you consider that the only reason Rob went to the junkyard in the first place is because the characters were dumped there. And the only reason the characters were there is because Toaster insisted on going out to find the damn master in the first place. There's more I could explain, but it's way too confusing to think about... On the other hand, if Toaster actually  this would not affect the human Rob in any way...until he went back and time and got into the same situation, effectively creating a Stable Time Loop. God, my head hurts...

The sequels are not canon
There's proof here: If Rob was such a good mechanic, why the crap did he decide to become a veterinarian instead? Talk about wasted talent... Also, I realized that in the sequels, things that shouldn't be alive are, such as a faucet (not electrical or mechanical) and a computer mouse (the mouse should simply be an appendage). My conclusion? The sequels are just figments of Blanky's imagination. Either that or they are being told by an Unreliable Narrator (possibly Lampy).
 * He was good at fixing appliances, so he decided to try fixing living things.
 * And Brave Little Toaster Goes to Mars is canon, it's in the book.
 * Considering that the first movie was about a talking toaster and every other scene was like a bad acid trip, is a sequel where they go to Mars that far-fetched? All the sequel meant to this Troper was that the writers did just a tad bit more LSD after making the fisrt movie, and decided to make another.
 * The director was not involved with the sequels and says he never even watched them. Interpret that as you will.

The whole movie is a huge dream sequence by Rob.
Either the adult or child Rob is having this dream. That part where they all wake up at the start of the movie? That's the beginning of the dream. If it's the adult, he's dreaming he's Toaster, and if it's the child, he's Blanky. This means that the appliances were never actually alive, as the movie didn't happen in real life.

The television set in St. Peter's broke himself.
Before all of the B-movie appliances went insane, they were all deperate to not meet the fate of their friends, so the television got one of the others to run into him, so although he looked broken and useless, he was still alive and less likely to be killed.

The Mish-Mash appliance was the result of surgery gone wrong.
Similar to the above WMG, Mish-Mash was one of the first to be a victim of St. Peter's, but they didn't want it to die so they tried to fix her by using the spare parts of other dead appliances. The results were disastrous results.

The Hanging Lamp in the junk shop is...

 * An altered/broken appliance, just like all the others. He was once a nice desk lamp, or tall living room lamp, and St. Peters' took his stand away and made him into a ceiling lamp. Anything creepy he tells the newcommers is either a warning to help their chances against Peters', or an attempt to cheer them up with black comedy humor. He gives Lampy his bulb as a genuine act of pity.
 * An unwilling observer. He was always a ceiling lamp and won't be harmed, because Peters just uses him to light his workplace. But he's still a good guy, and was just driven a bit mad from having to watch what was done to his inmates.
 * A sadistic observer. He enjoys watching other appliances get taken apart, and acts as a guard for St. Peters. When he laughs, "Do you hear that boys? They want to know how to escape!" its evidence that he's manipulated the others into thinking there is no escape. He gives Lampy his bulb because he has a soft spot for fellow lamps.
 * Same as above, only creepier. He gave Lampy the bulb just so he could watch him lose it again when Peters needs lamp parts. Any words of concern he voices for Lampy or the others is meant in a mocking way.

Radio is a Time Lord.
His TARDIS is his own casing.
 * How, exactly? Unless you're talking about the sequels.

The masters name is...
The Master.

The power that Elmo St. Peters had over his prisoners was psychological.
The creepy Peter Lorre lamp laughs when Lampy asks how they can escape the shop. The appliances seem to think escape is impossible. And yet, once Mr. St. Peters falls unconsious, they instantly yell "Jail break!" and the fridge crashes through the door with no trouble. Why couldn't they just have done that when Peters was off running errands, or something? There is only one explination; they were too scared to try. Seeing their friends get mutilated by Peters made them believe his power was invincible. Once seeing him defeated by the Toaster's group, they realized that Peters was not invincible--which inspired Mr. Fridge to think taht perhaps the walls weren't either.
 * He had a good ol' case of Fridge Brilliance!

Toaster died at the end of the first movie, and the sequels are his Dying Dream.
Really, he was clearly crushed beyond repair, and this explains the sudden change to a Lighter and Softer tone of the sequels. They are an attempt by Toaster to preserve his own sanity.

Toaster can Toast Toast.
You know what they say...

The appliances are prototypes for the ones used on Red Dwarf.
OK, only the toaster is shown as being able to talk, but I'm sure there are others not shown...

This movie is responsible for creating Hoarders.
You can never throw anything out after watching it.

All the nuclear weapons are alive as well.
And since all electronics in this world want to be loved and used by their master, and nuclear weapons have been doing nothing but sitting in a dark silo and not exploding for decades, with no one to talk to, they have gone insane. The world of The Brave Little Toaster is getting closer and closer to nuclear Armageddon, in which the nuclear weapons will finally be happy that they can be used.

Tinselina can warp reality.
She was originally a fairy, but her apprentice got annoyed by her Christmas spirit, turned her into a Christmas angel tree topper, and sent her to Mars. She went to the future to see if she would ever get back to earth and found out the Wonderlux appliances plans to blow up earth. They succeed. So Tinselina somehow finds out that Toaster and his friends can save earth but they died in the first two movies from... well... Logic. So Tinselina uses her reality warping powers to help our heroes survive long enough to save the world. Why doesn't logic work in this movie? Blame Tinselina.