The Dude is Kevin Flynn from TRON
His reign as CEO of Encom didn't last long. He quickly ended up on the streets and adopted the name of a famous millionaire so as to stay off the grid. He prefers to go by "Dude" because Jeff Lebowski is not his real name, he only uses it for taxes, unemployment, etc.
His apparent omniscience, plus his interactions with the Dude, indicate he's got powers beyond what his appearance would belie. He's a G-Man, and the events of the film were set up by him to further whatever mysterious purpose G-Men exist for.
When he's says that The Dude is a name no man would self-apply where he comes from, he's not referring to the Wild West; he's referring to Lyra's world. And those bears which sometimes eat you? Armored. To clinch it, they're both played by the same actor.
The Stranger is God.
He does seem concerned about The Dude's potty-mouth.
- That and if God were to appear in a Coen Brothers movie, this is probably how he'd be. Seriously, listen to that wise old voice of his.
- I don't think the Stranger is 'God' but maybe just a 'Watcher', someone who lives forever and watches people interacting. He then tells anyone will listen the stories he has witnessed in his long life. Who knows? He may be telling your story right now...
Walter wasn't in Vietnam.
- That would make him rather pitiful.
- This may actually be canon. In the script there is an extra scene: Donny's funeral. Here Walter makes a final 'Nam reference and the Dude replies, "Walter, you weren't even IN Vietnam."
- It would also fit in rather well with the movie's theme of almost everyone hiding their real identity behind a sham one.
The Dude's future kid is Donny reincarnated.
The baby was conceived pretty close to when Donny had his heart attack.
Walter was in on the deal the whole time.
Note how he's the first to claim Bunny kidnapped herself...
- Actually, The Dude himself was the first one to propose that possibility. Walter just latched onto it and refused to let go.
The Dude and Walter win the league tournament.
Larry Sellers really did take the money.
He bought a Corvette, and when he saw Dude and Walter pull up, he quickly called his neighbor and told him he'd give him $5,000 to pretend it's his car.
- Although the kid couldn't have taken any money, since the Big Lebowski didn't give them any money in the first place; all he gave them were phone books.
- You have your story, I have mine!
- Then again, it's never really explicitly stated that the Big Lebowski did that. That's just The Dude's theory. The whole thing is left in sort of an air of mystery.
- It's very heavily implied, though, but I do see your point.
Walter is really Dan Conner.
He decides to take up bowling and hang out with Jeff Bridges rather than visit his mother, luckily he's already in California. The whole "having an affair with his mother's nurse" thing is just a cover up because it seemed easier than explaining what really happened.
- Well Walter was married, maybe the affair was a bit more complicated then we thought.
- He did lie about being in Vietnam, after all.
The Stranger is the tumbleweed from the opening sequence.
He's a sentient tumbleweed that can shape-shift.
The Dude is Jesus and Jesus is the antichrist
I really got nothing I just like the theory.
Maude was "banging" Uli Kunkel (to use the parlance of our times).
At some point in the past the two were lovers. She knows a lot
about him, he seems to be no slouch with women, and she seems to have picked up a hefty disdain for men talking about their "johnsons" from somewhere. He also fits the deadbeat profile she outlines when she tells the Dude why she wanted to have his baby. Also? German nihilist techno-pop musician. This is Maude Lebowski we're talking about. Who else would she be with?
Maude is the Ubermensch, TBL is the Untermensch
Incredibly willful, and beyond good and evil. The Coens feature nihilism in this film, so Maude could be the Ubermensch, the being who has transcended the illusion of nihilism.
TBL seems to be an Untermensch. Think about it!
Uli does fix the cable in Logjammin'
We just weren't treated to that part. It happened after the sex scene. That's why Maude admonished The Dude for being fatuous because she asked him what happened next
The Dude is a Time Lord
Yes unlike most famous Time Lords he has a real name, but also like the famous Time Lords he's Quirky and has a moniker with the word "The" as it's first title.
Maude masterminded the whole plot
As explained here
Donny was dead the whole time
- Donny was actually one of Walter's buddies in Vietnam. He died tragically, with Walter watching as he died. Walter was really shaken up by that experience, and he felt guilty that he wasn't able to save his friend. Now, in the early 90s, Walter hallucinates that Donny is still alive. The reason he tells Donny to "shut the fuck up" all the time is because he's subconsciously aware that Donny isn't real (but he doesn't want to acknowledge that fact). The Dude is aware that Donny isn't real, but he plays along to keep Walter happy. No one else talks to Donny, because they're either not aware of the hallucination, or else they are aware but they're too creeped out to participate in the illusion. Nobody tells Walter that Donny isn't real, because then Walter would go nuts. A big reason why Walter is obsessed with Vietnam is because he feels guilty about Donny, though he can't mention that because then he would spoil his own illusion.
- When the nihilists attack, Walter is reminded of the night that Donny died. He's faced with people who have foreign accents who intend to physically harm him, just like enemy soldiers in Vietnam. A car is on fire in the background; in real life, an army jeep was on fire in the background. Confronting the memory of that horrible night, Walter is finally able to deal with his feelings. He says a few comforting words to fake!Donny, and defends him in combat. This allows Walter to absolve himself of his old guilt. Having achieved absolution, Walter resolves the hallucination by allowing Donny to die. (Notably, Donny is said to die of a heart attack. So it's not that Walter failed to save him from the attackers. In this version of Donny's death, Walter has no need to feel guilty.) The Dude is relieved to see that Walter is finally allowing fake!Donny to die. Walter hallucinates that an ambulance comes but that Donny dies anyway, and the Dude plays along. The Dude secretly goes to the crematorium ahead of Walter and has them prepare some fake ashes. (You could just burn some logs or whatever.) Either that, or the real Donny's ashes have been in storage at this crematorium for all these years. Either way, Walter gets some ashes, and he finally says goodbye to Donny.
- But if Walter also never fought in the war *head explodes*
- That's just a clever lie to throw you off track. It's all a conspiracy, man.
- Alright, let's work around that "You were never in Vietnam" remark. Walter wasn't in Vietnam, but Donnie was. Donnie signed up, but Walter was a draft dodger. Donnie died in action, and the circumstances of his death were explained to Walter later. Walter felt intensely guilty that he wasn't there to save his friend, and began to hallucinate.
- It's actually not true that Walter is the only one to speak to Donnie. The Dude does reply to Donnie, twice, in the same scene, when Walter does not react to what Donnie is saying. (That would be the "your phone's ringin', dude" scene.) But then, this could be from Walter's perspective, and he could, in fact, be speaking in Donnie's voice, alerting the Dude that it's "Donnie" speaking. But that takes it up a level from a mere hallucination.
Walter is the true antagonist
- When you look at the sequence of events that led to all the terrible things that happen in this movie, most of it goes back to Walter. His attempt to scam the kidnappers resulted in the nihilists being out to get The Dude, What we thought was Bunny's toe getting cut off (which wasn't actually hers), further complications with the rug, etc. Also, his poor handling of the situation with Larry's homework led to The Dude's car getting destroyed even further (which is what happens when you fuck a stranger in the ass).