I once played a few games against a Canadian I met, and at one point when he was starting a game as white he tried to play two different pawns each up one square instead of one pawn up two squares. Appearently he thought one had the option of moving a pawn two squares or two pawns one square each on the first move!
Crazy Chess Beliefs

Wow, that's a pretty extensive list. Not sure I have much to add. A few people I know think that you have to announce check when you deliver it to an opponent, or you lose. I've also known a few students who don't know that you can castle queenside.

since you mentioned en passant, would you kindly explain this move to me? I have a hard time understanding it and would appreciate your input. thank you

"Appearently he thought one had the option of moving a pawn two squares or two pawns one square each on the first move!"
Now that's weird. He must have been playing with Canadan Rules.
"A few people I know think that you have to announce check when you deliver it to an opponent, or you lose."
I played one guy a long time ago who thought unless you said check, the check didn't count.
en passant: if a player moves his pawn 2 squares on the first move and in the process passes by his opponent's pawn which has reached the 6th rank (so now the pawns are side by side) the opponent has the option to let it go, or to capture the pawn as if it had moved just one square (in other words, you can't move a pawn two squares on the first move to avoid capture by an enemy pawn - the capture is always an option)

I used to play casual chess games at work with a guy who thought it was cowardly to castle. He didn't think it was cheating, but he made all sorts of unpleasant noises whenever I castled to show his displeasure.
En Passante was always the big one with me and my "casual" chess playing friends.
But the pinned piece is an interesting one. I had quite a conversation with one opponent here on chess.com because he was quite sure chess.com had a bug. He wanted to move his king to a square that was covered by my pinned knight. His logic of course was, his king should have access to that square because by taking his king, I would be leaving my king in check, therefore it would be an illegal move.
The logic of course is faulty, but somehow this made perfect sense to him. I never heard whether he took it up with chess.com management or not.
Anyway, I've now been questioned by two individuals when trying to move a piece backwards. They were under the impression that like checkers, pieces can only move forwards. Usually this doesn't turn into a fist fight or anything, but it does take a minute before they believe I'm not trying to pull a fast one on them.

I must admit I can't fathom the confusion over the pinned piece, but it seems, if not common, a least not isolated either. Though I'm sure there are tons of things that confuse me that most people find obvious.
The curious part of all this is that chess really has few rules and most of those are refinements more than basic rules, yet if there's one thing that casual players have in common, its confusion over rules, often basic rules.
One common misconception even experienced players sometimes have is over insufficient material, and I think the one subsection that gives the most trouble is that you can't win with insufficient material unless your opponent resigns. If your opponent runs out of time and you have insuffient mating material even with worst play by your opponent, the game's a draw.

Sometimes beginners don't know that knights can jump over pieces, or when they learn that knights can jump over pieces they think that other pieces can as well.

A few people I know think that you have to announce check when you deliver it to an opponent, or you lose.
I've seen the perfect lesson (from Blitz and Bullet) to correct such mistakes: take the opponent's king with the checking piece!
It's also a forceful way to teach a beginner to look for threats immediately after an opponent's move instead of blaming somebody for it.

One of my OTB opponent was under the impression that if his pawn was situated in the diagonally neighbouring square to my pawn i had to take his pawn (like in checkers) and i didn`t have a choise of moving it past his pawn..yes, sometimes this kind of misinterpetations can cause a confusion

I'm surprised no one has mentioned the rules for castling, involving checks. Namely, that you can't castle into check (obvious), if in check (not so obvious), or if 'moving through' check (not at all obvious). But people tend to take correction on this point better than en passant. En passant is almost always looked at with suspicion by someone who doesn't know about it.
I suspect too, as mentioned above, that some people might not realize that, if the defending side's time runs out on a king vs two knights situation, that the defending side actually loses. Because, even though it isn't possible to force a mate, the mate possibility is still there. Even if the position is an obviously dead draw, if there is any mate whatsoever that is bizarrely possible, then the side that can be mated can lose on time. But then, most people that play timed games (sans internet, that is, where the rules of the game are upheld, and I don't have to be the one berated for explaining to my opponent why s/he lost) would be aware of these things.
And with that...I daresay the list is exhaustive. Maybe there's some REALLY bizarre beliefs that one or two people might have. I'd never heard of the Canadian idea mentioned above.

re cybermans comments on king vs king + 2 knights.I have one blitz game where i had the king only vs king + 2 knights. I offered a draw,pointing out that he is unable to force mate with king + 2knights but my opponent insisted on playing and for the next 45 or so moves he tried to checkmate me,before running out of time

I think the most common misconception I have seen in chess is about the 50-move rule. Even some veteran players from where I'm from seem to understand that it is 50-moves (some think 20-moves or 7-moves) "When one side has a lone king on the board" they don't realize that moving a pawn makes the countdown go back to zero (or capturing a piece which by the time there is a lone king would be impossible). It comes as a shock when I explain that it's 50 moves without moving any pawns or capturing any pieces regardless of there being a lone king or not.

re cybermans comments on king vs king + 2 knights.I have one blitz game where i had the king only vs king + 2 knights. I offered a draw,pointing out that he is unable to force mate with king + 2knights but my opponent insisted on playing and for the next 45 or so moves he tried to checkmate me,before running out of time
Which is a draw anyway. But kinda annoying when your opponent doesn't realize it, I imagine.
What would REALLY be frustrating is if your opponent had the two knights and you were in time trouble.

Castling: King has to be on e1, rook on h1 or a1 and pieces must not have moved. One opponent thought if you moved the king or rook to another square (Kd1, for example), then back to the original square, you could still castle.
This would be perfectly reasonable; it's just not correct.

I once played a few games against a Canadian I met, and at one point when he was starting a game as white he tried to play two different pawns each up one square instead of one pawn up two squares. Appearently he thought one had the option of moving a pawn two squares or two pawns one square each on the first move!
My Mexican brother-in-law tried the same thing, his first move was 1. a3h3!! And I remember some of my friends doing it when I was younger, so I don't think this made-up rule is all that uncommon. He also thought that instead of castling, that his king and queen could trade places.

An International master I knew still made the shape of an L when moving his knight..perhaps he didn't know any better and nobody told him!

Last year at the chess sectionals for my high school a friend of mine encountered someone who believed "check" needed to be stated for it to be valid. He also didn't realize that touching a piece obligated him to move it, if possible. The arbiter had to be called because something similar to the following position arose.
I was reading the forum topic "Pinned Knights Capable of Check," which explored the question of whether a pinned piece (or one restrained from moving) could deny an enemy King an escape square.
It caused me to think about some of the unusual conceptions some of my opponents have had about the rules of chess when playing OTB.
I think the most common one has been the 50 move rule. It seems to me that very few casual players (and by casual, I don't mean beginners - some have been playing longer than I've been alive, just not formally) I've met have a clue about that one. Many players seem to not understand en passant and a few have accused me of cheating when I've used it.
I know a couple times I played with people who didn't understand the rules of castling and very, very few casual players I know abide by the touch rules; some have even tried to take back moves as I was making my own. Some players don't realize you can promote a pawn into any other piece except a King (nor another pawn, which isn't really a piece), even if you still have the original complement for that piece on the board.
I could probably recall some other misconceptions, but I'd rather here what others have experienced.