Perhaps John Wayne's greatest role, and the one for which he won an oscar.

True Grit
(1969)

In a drunken rage, Tom Chaney murders and robs his employer Frank Ross. Chaney flees to indian country.  Ross's daughter, Mattie, wants him brought to justice.  The local sheriff has no jurisdiction and directs her to the U.S. Marshall.  She hires marshall Rooster Cogburn (John Wayne) to go after Chaney.  Texas ranger LaBouef (Glen Campbell) is also after Chaney for shooting a senator in Texas. They team up and head into indian country, where Chaney has joined up with Ned Pepper (Robert Duvall) and his gang. Ned Pepper catches Mattie.  He and Rooster cut a deal where Ned and his gang can escape if they leave Mattie unharmed. Chaney is left guarding Mattie, while Ned and the gang leave.  Ned has threatend Chaney, but Chaney intends to kill Mattie as soon as Ned is out of earshot.  LaBouef sneaks around and rescues Mattie from Chaney. When LaBouef hollers to Rooster, Rooster alone cuts off Ned and 3 others escaping.  Chaney surprises

LaBouef and kills him. In trying to escape, Mattie falls in a dry well with rattlesnakes. Rooster comes back and kills Chaney.  Rooster gets Mattie back to town and the doctor fast enough for her to be saved.

Thanks Joseph!

Joseph also adds...
The movie also has some great lines such as, "If I smelled as bad as you I wouldn't live near decent people".
Also the great sequence where Rooster faces off alone against Ned Pepper and his gang:
Ned Pepper: What's your intention? Do you think one on four is a dogfight?
Rooster Cogburn: I mean to kill you in one minute, Ned. Or see you hanged in Fort Smith at Judge Parker's convenience. Which'll it be?
Ned Pepper: I call that bold talk for a one-eyed fat man.
Rooster Cogburn: Fill your hands, you son of a bitch.