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Trivia from Raging Bull:

Original script included a scene of La Motta masturbating in his prison cell.
Sound effects for punches landing were made by squashing melons and tomatoes. Sound effects for camera flashes going off were sounds of gunshots. The original tapes were deliberately destroyed by the sound technicians, to prevent then being used again.
The scene by the chain link fence where Jack meets his girlfriend was ad-libbed.
Robert De Niro accidentally broke Joe Pesci's rib in a sparring scene. This shot appears in the film: De Niro hits Pesci in the side, Pesci groans, and there is a quick cut to another angle. See also Casino (1995).
Jake (De Niro) asks Joey (Pesci) “Did you fuck my wife?” Director Martin Scorsese didn't think that Pesci's reaction was strong enough, so he asked De Niro to say “Did you fuck your mother?” Scorsese also did not tell Pesci that the script called for him to be attacked.
To visually achieve Jake's growing desperation and diminishing stature, Scorsese shot the later boxing scenes in a larger ring.
De Niro gained over 50 pounds to play the older La Motta, and Pesci lost weight for the same scene.
Directors Cameo (Martin Scorsese): asking Jack to go on stage.
In preparation for his role, Robert De Niro went through extensive physical training, then entered in three genuine Brooklyn boxing matches and won two of them.
To show up better on black-and-white film, Hershey's chocolate was used for blood.
Original script was vetoed by producer Bach, after he told Scorsese and De Niro that LaMotta was “a cockroach.” De Niro and Scorsese did an uncredited rewrite of the script to make LaMotta more human.
Although only a few minutes of boxing appear in the movie, they were so precisely choreographed that they took six weeks to film.
Joe Pesci, at the time a frustrated, struggling actor, had to be persuaded to make the film rather than return to the musical act he shared with fellow actor Frank Vincent.
Scorsese's father Charles is one of the mob wiseguys crowding the LaMotta brothers at a Copa nightclub table.

Quotes from Raging Bull:

Jake LaMotta: I get ya's both in the ring, I'll give ya both a fuckin' beatin', ya both can fuck each other.

Jake LaMotta: You punch like you take it up the ass.

[Sugar Ray Robinson has just battered Jake La Motta half to death, but Jake has stayed on his feet]

Jake La Motta: You didn't get me down, Ray.

Joey LaMotta: [to Jake LaMotta] If you win, you win. If you lose, you still win!

Jake LaMotta: Did you suck Joey's dick?

Vicki LaMotta: No, I didn't suck Joey's dick!

Jake LaMotta: Did you suck Joey's dick?

Vicki LaMotta: No, I didn't suck joey's dick!

Jake LaMotta: Did you suck Joey's dick?

Vicki LaMotta: Yeah I sucked it! I sucked his dick! And you know what? His cock is bigger than yours!

Jake La Motta: I remember those cheers they still ring in my ears, and for years they'll remain in my thoughts. Cuz one night I took off my robe and what'd I do, I forgot to wear shorts. I recall every fall, every hook, every jab, the worst way a guy could get rid of his flab. As you know, my life was a jab...Though I'd rather hear you cheer when I delve into Shakespeare. A Horse, a Horse, my Kingdom for a Horse, I haven't had a winner in six months. I know I'm no Olivier, but if he fought Sugar Ray, he would say that the thing ain't the ring it's the play. So gimme a stage where this bull here can rage. And though I can fight I'd much rather recite That's entertainment. That's entertainment.

Cast overview, first billed only:

Robert De Niro .... Jake La Motta

Cathy Moriarty .... Vickie La Motta

Joe Pesci .... Joey La Motta

Frank Vincent .... Salvy

Nicholas Colasanto .... Tommy Como

Theresa Saldana .... Lenore

Mario Gallo .... Mario

Frank Adonis .... Patsy

Joseph Bono .... Guido

Frank Topham .... Toppy

Lori Anne Flax .... Irma

Charles Scorsese .... Charlie - Man with Como

Don Dunphy .... Himself/Radio Announcer

Bill Hanrahan .... Eddie Eagan

Rita Bennett .... Emma - Miss 48's