Monsters, Inc./WMG

Children really are toxic
To monster's anyway. They limited the amount of exposure necessary to harm them in the film.

Boo's real name is Emily.
And in ten years or so, when she gets too old for dolls, she will leave the Cowgirl Jessie doll she showed Sully in a box for charity in the park, as seen in the flashbacks in Toy Story 2.
 * Genius.
 * Nope, but still same universe. Issue 3 of the Monsters Inc. comic features Sid as a villain, sneaking through active closet doors stealing toys after what happened to him, including Boo's Jessie doll.

Boo's real name is Violet.
Specifically, Violet Parr. Her ability to get places she shouldn't be without Sully noticing is due to her invisibility powers just beginning to manifest.

Word of God says that her name is Mary.
 * Boo might still be Violet even if her real name is Mary. After all, a girl as angsty as Violet certainly wouldn't want a plain name like Mary; she would change it, if only by refusing to answer to it.
 * Violet's invisibility doesn't affect her regular clothes, though; Her Suit Is Also Super.
 * I had always assumed that she got her sneakyness from Randall. It is explicitly stated that Randall is Boo's monster, and maybe his powers rubbed off on him.
 * I think it's less "powers rubbing off" and more "watching him and learning his tactics".

Boo's real name is Chell.
Her constant vanishing act throughout the film shows that she's clearly thinking with portals. Plus, she and Chell look similar.
 * And then, on one fateful take-your-child-to-work-day Take-An-Obscure-Relative-To-Work-Day...
 * Now illustrated for your viewing pleasure: http://melancholy-meloy.deviantart.com/#/d4wc77h

Changing the power source to laughs will result in our world being drained of laughs and drowned in laughter.
Everyone will become a cold, atheist soulless executive emo. Previously, humans could be happy because the monsters were purging our world of scariness. ** Even if some things never stop being funny, people may stop expressing their enjoyment aloud. It's like, just because some things are always erotic, doesn't mean people will start doing it in the road if some ad company puts it on a billboard.
 * Who says that they'd be atheists? Maybe they'll be a people so consumed by their religion that they are afraid to laugh or have any sort of fun again out of fear that their God will smite them... and hey, now that they're all terrified again, the monsters would be free to start using screams for power again! And so the cycle continues.
 * HA! Laughter and fear are obviously unending, renewable sources. Some things never stop being funny. And what about Nightmare Fuel? People are still scarred from that.
 * They only go after kids, not adults, so comedians will have a harder time when the kids grow up. Not the monsters' problem. Or alternatively, the kids might learn to laugh; the only problem might be older kids exposing their siblings or friends to jokes, but some monsters just look funny and older kids can't emulate that.
 * It gets worse. Because of the huge spikes in energy demand from developing countries, people will be forced to work in sweatshops where they just watch funny YouTube videos all day. Laughing at home is strictly prohibited because it is wasteful.
 * So, that's the origin of the Anti-Spirals?
 * Conquering people to make them work in sweatshops: hard. Laughing gas and a cup of water: easy. Like the scream extractor but with laughs.
 * Alternatively, it could have the opposite effect of making people happier and generally less stressed. Think about it, someone doesn't stop laughing nearly as soon as they stop being afraid. Thus they could actually keep the process up a lot further. So elementary and possibly high school students might be far less stressed.
 * I don't know what atheism has to do with anything and I find it kind of offensive that you imply that it is a bad thing.

At the end there's both a laugh and scare floor
Comparing the main tower you see in the middle of the complex in the full shot of the factory with the overall shape of the scare/laugh floor, it looks like there's two different scare floors in the beginning. Also, some monsters are more thoroughly trained as scarers and it'd be easier to have half of your floor with already trained professionals while getting used to the new system of using laughs.

It's not a Kids' movie at all
It's not about two monsters and their adventures with a human kid. The entire film is a biting political satire about the California energy crisis of 2000/01, the underhanded tactics of Enron, and the need to replace nuclear fission with fusion.
 * Alternatively, it's a reference to the War of Currents between DC and AC electrical power.

The doors are alive.
The doors require every large piece to function properly, but at the end, Boo's door still clearly displays the cracks from being shredded. When Mike adds the final piece, he closes a relatively large, irregularly shaped gap. (All of this only occurred to me because I was reading Slaughterhouse V.) As per the cryptic parenthetical, the door can function with cracks (live with slit-shaped wounds) visible, but can't handle missing pieces (in the reference, triangular wounds, but more generally chunks of flesh ripped out--charming, eh?)

Boo is a Slayer.
...who just got activated really, really early. Explains the whole 'beating the holy hell out of the villain thing'.

Aaahh Real Monsters takes place in the same verse'.
Why does ''Aaaah! Real Monsters'' take place in our world when the monsters in the film live in a different universe you ask! The School is located in our world so the students can get some first hand experience. While the monsters train at the Academy as students, they later find jobs at Monsters Incorporated.

Boo is Haruhi Suzumiya at a younger age
She used her  to make monsters become real and happened to end up with Mike and Sully.

Boo is Russel's mother from Up at a younger age
And nothing more.
 * Russell's mother is Asian. Boo is caucasian.
 * I don't believe Boo's race was ever stated.

The monsters speak a different language than humans do.
Boo walks, runs, is toilet-trained, and draws remarkably realistic pictures for a young child. I'd put her age somewhere between 3 and 4. Despite this, most of her dialog comes out as gibberish. My theory is that the movie translates the monster language for convenience. This would explain why all we can understand from Boo is "Kitty!" (which must be the same in both languages, for whatever reason) and "Mike Wazowski" (which she learned from Sully). It is also a possible explanation for why the kid at the very end doesn't laugh at Mike's act until he swallows the microphone.
 * Word of God states that Boo is 2.

Boo in the sequel
The sequel will be set 10 years after the first film and Boo is a moody Goth teen in vast contrast to how she was as a toddler.
 * I thought that if Boo was going to be in the sequel she'd be a Perky Goth sort of like Lydia from Beetlejuice.
 * I thought she might grow up to be a Deadpan Snarker.
 * Jossed.

The use of laughter for energy will destroy the monster world.
Imagine you have a large group of kids being scared by monsters. A decent percent of them will complain to their parents about this. Now imagine the same kids telling their parents those same monsters are trying to make them laugh. That would have dangerous consequences for the monsters, wouldn't it?
 * I'm not sure what you're getting at - plenty of children have benign imaginary friends. Many parents would probably assume that the kid has gotten over their fear of whatever caused them to imagine the monster in the first place, and traded the "scary, threatening monster" fantasy for a "friendly, funny monster" fantasy. Not to mention that most of them won't have the same monster in both roles, as it's implied that most of the scarers aren't really suited for laugh collection.

The snow cones weren't lemon-flavoured
The Abominable Snowman leaves, supposedly to give Mike and Sully privacy.You can clearly see he gets scared easily, so pants-peeing isn't implausible(this takes care of the source).As Sully sleds his way to the town, he comes across the Snowman who now has a new batch of snow cones. If they were lemon-flavoured,then where did he get lemons from?Lemons don't grow in regions as frigid as the Himalayas! He couldn't have gotten them from the town either, as it was a "Three day hike away".Also,this might not have been improper of him,as Monster society probably had such flavours(remember,they have deodorant scents like "Wet dog"). On a side note, the Snowman was probably banished from the world of monsters because of his tendency to get terrified, which was unMonster-like behaviour.
 * It's possible he could have gone down to the village and gotten lemon snow-cone syrup.
 * Don't Explain the Joke
 * Actually, when the Snowman was coming back up to the cave, the sno cones were just plain snow.

Boo can teleport
There is no other explanation for how she can disappear without a sound and then be right behind or in front of you.
 * You and the other people whose theories solely explain Boo's teleporting act have clearly never had or watched small children. Boo's ability to suddenly be where she shouldn't is only very slightly exaggerated for a child her age. Unless, of course, you are implying that all young children can teleport, which is quite plausible.

Boo is a god of the monsters world
Think about it. When she cries, she almost caused a power outage, but when she laughs, the electrical power increases.
 * So... all children are gods in the monsters world?

At one point, Monsters Inc. had a run-in with Aperture Science.
It explains how the doors are able to act as passageways to rooms in the human world - the doors were created using the portal gun technology.
 * Is it just me or does Atlas from Portal 2 look like a robot version of Mike?

The monsters will eventually lose technology due to lack of laugh or scream power
Following the idea that all Pixar films take place in a shared universe, in hundreds of years, the monsters will lose the ability to make technology since all of the humans have left Earth on the various Buy 'N Large cruisers. This probably means that the monsters will either die out or revert to primal instinct in order to survive.
 * ... Or they could just find a different energy source. But I suppose your idea is more interesting.
 * Or they could just use the doors on the Axiom! They're already dimensional doors, and they don't have to "line up" with each other (the monster-world sides move around all the time). If there's a general distance limit, then they may need to build their own spaceships and leave along with the humans.

The prequel will explain why and how the Abominable Snowman was exiled.
John Ratzenberger has been confirmed to appear in the sequel.
 * Of course he has. He's in every Pixar film. Doesn't necessarily mean he'll reprise his role as the AbomSnow.

The humans are going to find the monster world, one way or another.
The door-vault sequence, with the number of doors it opened and the number of people who saw monsters go through, probably revealed at least one door to the human world. And the very act of going through a door and making the kids laugh, which usually takes longer, is fraught with peril–the monsters have to stay outside their world longer, which means that there's a greater danger of being caught on CCTV/satellite imaging/news video. Discovering a portal to another world through which Starfish Aliens come would be a huge event for humanity–doors would probably be guarded and filmed, waiting for one to open so that scout/assault/research teams can enter. What the humans will do is uncertain, but it's likely that something monumental will happen.

Randall is also |Andy's monster.
When Fungus pulls down a variety of backgrounds for Randall to "warm up" with, one of them is Andy's wallpaper from the first Toy Story.
 * This troper thinks there should have been a scene during the running-through-doors sequence where Mike and Sully open a door that leads to Andy's bedroom, leading to a "this is weird" moment between the toys and the monsters.

The Backson from the 2011 Winnie the Pooh movie is a Monsters Inc. Scarer that got stuck in the human world.
Was I the only one who thought he looked like a character from Monsters Inc.? Maybe he was a top scarer before, who through an accident got locked outside of a closet in England, and decided to roam the 100 Acre Woods to find a way home.

Mike and Sully weren't the first to discover the power of laughter.
Back when power was invented monsters realized that laughter was more powerful, but either, a corrupt corperate executive already designed a scare system and hushed the competition, or it seemed cool in theory but too powerful/unstable and didn't implement well with the current teckoledgy.