My favorite Marlon Brando credit is his appearance in the play "I Remember Mama" as Nels, the brother. I really don't know why.
Brando was the perfect movie star for the '50s; with the collapse of the studio system and the rise of television, the movies were desperately looking for something new, something to distinguish themselves from television. They came up with CinemaScope, the long-overdue loosening of the Production Code, location shooting -- and Marlon Brando. His acting style was "in" both with critics and audiences. (It's been pointed out that many of Hollywood's favored genres of the '50s -- the epic, the gritty shot-on-location drama, the stage adaptation -- were more or less "midcult" genres, an attempt to make Hollywood movies the respectable, higher-class alternative to the "lowbrow" televsion programs. Co-opting the ultimate midcult acting style, the Method, was just part of that whole process.) Even his easily-parodied mannerisms of speech and movement were all to the good, as a star who can be parodied is a star who is distinctive, and Hollywood was having trouble coming up with distinctive new stars, people who really stood out. Method Acting is easily parodied today because we're in a better position to understand its limitations, and to celebrate the old-school, "just get on with it" style of screen acting. But in 1951, that style of screen acting seemed just too hopelessly old-fashioned, too closely identified with the lost studio-system era. Brando offered something fresh in a film industry that had lost confidence in the old ways. He would lose his way, as a star name, when he signed his first exclusive contract with a studio, a disastrous deal with Universal in the '60s. Brando wasn't cut out to be a studio contract player; his mystique was dependent on his independence.
I haven't seen a lot of his movies recently so I can't really comment on what I think of his individual performances. I certainly think his performances in Streetcar Named Desire and On the Waterfront are excellent, though among Elia Kazan's movies I'd rather see a DVD of A Face in the Crowd (starring a very non-Method actor, Andy Griffith). He's really not all that embarrassing in Superman, and like many people I'd like to see a recut of Superman II with Brando's scenes restored (many important scenes were removed by the producers after they fired the original director, Richard Donner). The Freshman, which Brando famously condemned as a piece of trash while he was filming it, is a wonderful comedy that testifies to the onetime promise of Andrew Bergman, though Brando's performance is not one of the better things in it.
Joe Queenan nominated Brando's accent in the remake of Mutiny On the Bounty as "the single worst accent in cinema history," noting also that Brando and Laurence Olivier were the two all-time great masters of the truly bad accent. Queenan ultimately gave Brando the edge for "the utterly serendipitous nature of his bad accents," since while Olivier's terrible accents were usually at least somewhat related to the character he was supposed to be playing, Brando's bad accents often made no sense whatsoever, in that you couldn't always tell what country he thought he was supposed to be from or why this particular character would ever talk like that. With Brando and Olivier both gone, the art of the bad accent may never be the same.