A Stock Phrase. Alice has just done something/been somewhere/went on a crazy adventure, and Bob asks her about it, usually with "Where Were You?" Rather than boring the audience with the story, or using a quick Fade Out-Fade In to skip it, Alice simply says "You Wouldn't Believe Me If I Told You..."
And It's a Long Story, anyway...
A common variation (or addition) is: "I wouldn't believe it myself if I hadn't seen/lived/heard/witnessed/experienced it." And as the examples show, there are several permutations of this sentiment.
The opposite is Cassandra Truth, where Alice does tell Bob, and Bob doesn't buy it. Related is Sarcastic Confession, where Alice tells Bob in a sarcastic manner to prevent him from taking it seriously. Contrast Suspiciously Specific Denial.
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Anime & Manga
While never actually said in Code Geass, this trope is the likely reason why Lelouch never explains to Suzaku that his Geassing of Euphemia was an accident.
A major plot of G Gundam is that Kyoji made a clone of himself with all of his knowledge and skills in order to protect his brother Domon as he was currently under the control of the Dark Gundam and incapable of helping Domon himself. When asked by Domon why he didn't reveal this secret earlier, Kyoji's clone states, "You were so hot-headed back then, Domon; you wouldn't have believed me if I had told you."
In Digimon Tamers, the Tamers would try to keep the Digimon secret from their parents as they wouldn't believe them.
In Puella Magi Madoka Magica, this is the reason Homura gives as to why she never told anyone about the terrible secrets behind Magical Girls. And she knows this for a fact: in previous timelines, she did try telling her friends, but they never believed her.
Played with in The Lion, the Witch, and the Wardrobe when the Professor finds the kids just as they return through the wardrobe from Narnia after spending years there. When they give his stock line, the Professor (who went to Narnia himself as a boy) playfully responds, "Try me."
The Final Countdown uses the, "They're never going to believe it," variation as the USS Nimitz is returning to Pearl Harbor, having just spent about a week in 1941 thanks to Time Travel.
Live Action TV
In Pushing Daisies, Chuck tells Ned that Olive wouldn't believe that Ned had brought Chuck back to life even if she told her. Ned asks her how she knows that, and she says, "because I told her and she wouldn't believe me."
Used in Buffy's second season finale, after Spike has offered to help her prevent the apocalypse.
At the end of the classic Doctor Who episode "The Three Doctors", a man is zapped back to his small English village after being accidentally sucked into one of the show's typical plots. His wife appears and starts peppering him with questions about where he disappeared to. He listens stoically, then grunts "You'd never believe me, woman. Supper ready?" and stomps into his house.
It's also a common reply by the Doctor himself in regards to questions like "How did you get here?", "How do you know that?", "What makes you think our benevolent leader (who is actually The Master) is up to something bad?" and so on. The few times he does tell, people predictably don't believe him.
Used by Richard in the LOST episode "Dr. Linus"; like the Professor above, Jack responds "Try me," as a) he has been through an awful lot of weird shit, and b) he is getting a bit sick of people dodging questions.
In an episode of Full House, Jesse receives some timely advice from a man who looks like (though hinted it might be) Elvis Presley, and when Jesse mentions he looks familiar, the stranger says people mistake him for Wayne Newton. When Jesse is telling everyone else about the stranger, he realizes that being a huge Elvis fan, it was just too weird that he got advice from a man who looked like Elvis, so he said the man looked like Wayne Newton.
So Random!: Rufus's Catch Phrase is "Oh, you're not going to believe this." Naturally, every word he says is true, no matter how ridiculous.
Sliders had this nearly every episode, when they had to convince people in whatever Alternate Universe they were visiting of where they came from.
Early Edition had this fairly often too, when Gary Hobson, a man who gets tomorrow's newspaper today, is asked how he knows that things are going to happen before they do.
A variation: In The Bible, Luke 22, the arrested Jesus is interrogated and asked to confirm that he claims to be the Christ. He answers with pretty much this phrase. If Our Lord being a Deadpan Snarker distresses you, wait 'til you find the puns.
A slight variation is said by Shay Bourne to Father Michael in Jodi Picoult's Change of Heart:
They moved to the far side of the room, and I leaned closer to Shay.
"Are you okay?"
"You wouldn't believe it if I told you."
"Oh, try me."
Happens in The Dresden Files novel Changes, where the Good Cop is questioning Harry about a building that was bombed. Harry delivers this line when asked if he knows who did it, then the two change subject and talk a while before the cop decides he's innocent and lets him go. Before Harry leaves, the cop asks who really did it, to which he responds "Vampires," adding "I told you you wouldn't believe me" a minute later when the cop goes through surprise and disbelief.
In WebMage, Ravirn is placed under a "Cassandra Curse" that prevents people from believing anything he says about the Big Bad. When Eris tries to question him about a related matter, he tells her that she wouldn't believe him if he told her — which she naturally doesn't believe.
At the end of Conkers Bad Fur Day (And the remake.) Conker says this exact line to the bartender when asked "Ya look horrible! what happened to you?" Before being poured a glass of scotch and asking for the whole bottle.
The player can invoke this in Mission Critical after waking up with the first officer of the USS Lexington angry, holding a sidearm on them, and demanding answers. It goes about as well as one would expect.
At the beginning of the Warden's Keep DLC for Dragon Age: Origins, you can ask Levi Dryden how he was able to pick his way through a series of mountain tunnels to Solider's Peak. He utters this phrase in response, but when you press him, he reveals that it came to him in a dream. It turns out to be true; that was how the mage Avernus reached out to Levi, encouraging him to search the (not entirely) abandoned fortress.
In King's Quest V: Absence Makes The Heart Go Yonder!, Graham gets carried away by a giant Roc and is only barely rescued from being eaten by its young by a friendly eagle, who deposits him on a beach. When Cedric asks where Graham went, he responds with the trope name.
Which is rather odd, seeing as in that game alone he dealt with genies, witches, magic ice queens, elves, gnomes, talking animals and trees, yetis and gypsies. But getting carried away by a giant bird is apparently too much to believe.
During the final level of Crysis Nomad finally meets with Psycho again, who had been supporting him throughout the game up until they were separated, and sees that he has secured an alien life-form for the U.S Navy to study. Nomad asks Psycho how he got the alien off the island and onto a Naval vessel Psycho responds saying, "Long story. You wouldn't believe me if I told you." However there was a DLC for the original PC version where we do in fact see how Psycho got it.
In Persona 4, this trope is the reason why the Investigation Team (a ragtag group of high school kids) can't turn to the police for help. Which is proven true late in the game when the Protagonist gets hauled off to Police Station by Dojima (his uncle and a detective) after receiving a threat letter in the mail.
Doug episode "Doug Takes the Case/Doug's Secret Song"
Scooby-Doo! and the Goblin King. At the end of the episode, the benevolent Goblin King casts a spell that erases memory of the night's events from everyone but Shaggy and Scooby. When the rest of the gang asks what happened, they use the trope.
In the Justice League Unlimited episode "Double Date", Green Arrow asks The Question why he's helping Huntress track down the man who killed her parents. Question responds with this, and everyone just assumes he says it because his motives are something insane. (It turns out he's just trying to impress Huntress.)