The Big Lebowski. The Dude. Not much gonna run better than that.
We can do some runner ups:
The guy who died while jerking it in the bathroom in Clerks, and the girl thinks it’s her BF with the lights out and she fucks his corpse.
The man in black/the dread pirate Roberts/ Wesley from Princess Bride.
Edit- clerks 2, kinky Kelly and the sexy stud and the nomenclature confusion.
The Big Lebowski
The Life of Brian
North by Northwest
Not comedic, but *The Talented Mister Ripley.*
Scam artist gets mistaken for the friend of a rich man's son, so the rich man pays the scam artist to go to Italy and convince the son to return. More mistaken identities and deliberate impersonations pile up and snowball into a trainwreck.
**Some Like it Hot** has to be the absolute best example of this.
Others: *School of Rock, The Big Lebowski, Zelig, North by Northwest, The Great Dictator*
The Wrong Guy (1997). After an assassination, a witless witness thinks he's the prime suspect. The assassin thinks the witness is a supercop after him. And the witness keeps ending up in circumstances to support this as he runs from the law. However, the cops are in no way chasing the witness; they figured out immediately that he was just some guy. It turns into a really absurd kind of cat and mouse.
I'm shocked that no one has mentioned "[Dirty Rotten Scoundrels](http://www.imdb.com/title/tt0095031/)".
Not exactly my #1 favorite but I'm gonna mention this because no one else has yet:
*The Wrong Man* (1956) directed by Alfred Hitchcock
Not sure this one counts as for comedic purposes, but Catch Me If You Can is the first one that comes to mind for me
not particularly comedic (well not at all) but Primal Fear is unreal :)
Completely agree with the other comments about Big Lebowski and Some Like it Hot!
I'd like to add While You Were Sleeping.
Momento...but..kinda of doesn't count if you are mistaken for yourself...
More recently, Good Time has something similar. Not exactly someone who fakes their identity but someone who gets mistaken for another peraon.
Dumb and Dumber is amazing for the antagonists believing the two protagonists are hitman when they are really just incredibly stupid bystanders.
Not a film but Changnesia from Community is always funny as hell
I like the 1993 Branagh version best as far as film goes, but you can’t beat “Much Ado About Nothing” for nonstop mistaken identity hijinks. But Shakespeare is full of that and honestly it never gets old.
The Majestic. Not exactly what you asked but same principle. It is a mistaken identity thing that goes too far, but it's done as a result of Jim Carrey's character's amnesia. I remember really liking this movie, but I haven't seen it in a long time.