Zelig

A 1983 Woody Allen film, Zelig is a Mockumentary set during The Roaring Twenties and into The Great Depression period, concerning the title character, a "human chameleon" -- a man who shapeshifts to fit in with those around him -- and his encounters with the celebrities of the day. Zelig ultimately comes into contact with Dr. Eudora Nesbitt Fletcher (played by Mia Farrow) who tries to cure him of his uncontrollable shapeshifting. Throughout, commentary on Zelig's life is provided by well-known public intellectuals.

See also The Gump, for which The Zelig is the alternate trope namer (and ur-example).

Not to be confused with the Italian comedy show, which has the same title.

Tropes used in Zelig include:

All Psychology Is Freudian: Kind of mocked in that when first receiving treatment, Zelig takes on the persona of a psychiatrist and makes comments that echo a Theme Park Version of Freud.
Amnesiac Dissonance: Zelig is ultimately confronted with various victims of his shapeshifting- women he impregnated, a guy he performed surgery on, etc., none of which he remembers doing.
Black Like Me: Zelig can alter his race.
Blank Slate: Zelig starts out as this, having no real personality of his own outside of the various identities he uncontrollably adopts (and has no memory of afterward)
Celebrity Paradox: The movie does a good job of justifying why its audience would never have heard of Zelig by treating him as one of many fads of the 1920s and 1930s, forgotten when the public discovered something new of interest.
Crowning Moment of Funny: After Zelig returns to America after falling in with Those Wacky Nazis, by becoming the first man to fly over the Atlantic Ocean entirely upside-down:

Zelig: It shows exactly what you can do, if you're a total psychotic!

Earn Your Happy Ending
Feigning Intelligence
Freudian Excuse
Hilariously Abusive Childhood: As recounted by Zelig under hypnosis, "My brother beat me. My sister beat my brother. My father beat my sister and my brother and me. My mother beat my father and my sister and me and my brother. The neighbors beat our family. The people down the block beat the neighbors and our family."
I Have This Friend: When Dr. Fletcher starts out trying to treat Zelig, he is unresponsive and takes on the persona of a psychiatrist. So, she pretends to be a patient asking about a problem of a "friend" -- while she "admits" that she is describing herself, she's actually describing Zelig's own problems, which unsettle him enough to break down his persona.
Involuntary Shapeshifter: Zelig's subconscious desire to fit in with the people around him causes him to actually physically transform as needed to seem like just another part of the crowd, including suddenly becoming obese or black.
Kavorka Man: Zelig seduced numerous women.
Know-Nothing Know-It-All: Pretty much, Zelig's character/Freudian Excuse is this trope taken Up to Eleven. Because of his desperate need to fit in, Zelig started out by pretending to have read Moby Dick when he hadn't, and this spiraled into mirroring the professions and even appearances of those around him.
Literary Agent Hypothesis: See Celebrity Paradox.
Master of Disguise: Zelig is somewhere between this and Involuntary Shapeshifting...
Mistaken for Special Guest: See The Zelig.
Mockumentary: Probably Woody's most accurate, as it never breaks the illusion that it's a documentary.
Older Than They Think: The idea of having a fictional character meeting tons of famous people (and altering photos and videos to make the fictional character look real) is associated with Forrest Gump, but this movie popularized the concept.
- Though Gump was to first to actually have the new character physically interact with historical figures; Zelig is always fairly obviously pasted into the old footage and never interacts with it.
Retraux: Lots of (remarkably convincing) fake 1920s and '30s footage -- filmed with authentic period equipment.
Running Gag: Moby Dick
Seemingly-Profound Fool: Zelig is somewhere between this figure, and a Know-Nothing Know-It-All.
Shiksa Goddess: Dr. Fletcher is fairly plain (well, Hollywood Homely), but this trope applies in that Zelig is Jewish (and lower class at that), while she is from a wealthy WASP background.
Those Wacky Nazis
Unusually Uninteresting Sight: Zelig's shapeshifting is regarded as little more than a curiosity, rather than prompting intense scientific investigation.
The Zelig: Trope Namer, an alternate title for The Gump.