The actor suffered from advanced dementia that set on after a series of dental operations in 2007.
Mr. Falk was 83 at his death—a number that may come as a surprise to his fans, given the actor was playing middle-aged and older characters while still a young man. But Mr. Falk's ever-rumpled appearance, drawling delivery and glass eye (a facial element that lent intensity to Columbo's unwavering gaze) added years—and seeming life experience—to his portrayals.
To the novice criminal, Lieutenant Columbo, a homicide detective with the Los Angeles Police Department, didn't appear to have much on the ball. He was stooped, disheveled, and wore a dirty trenchcoat badly in need of ironing. (Mr. Falk used his own clothes in the series.) He was forever touching his hand to his forehand in forgetfulness. This led suspects to underestimate him. But Columbo missed few clues and invariably brought his man in, with apparent ease and a rambling closing speech. To hear the Lieutenant say "Just one more thing..." was to feel the noose tighten around your neck.
Mr. Falk won four Emmy awards for his work on the show. The show began as a recurring segment of the "NBC Mystery Movie" rotation, from 1971 to 1978. Thereafter, the actor revived the character in occasional TV movies.
Mr. Falk was already an established character actor before "Columbo" made him a star. He studied with famed actress Eva Le Gallienne, who encouraged him to quit his job in Hartford and pursue acting. In 1956, he appeared at Circle in the Square in the famous revival of The Iceman Cometh with Jason Robards, playing the bartender. He made his Broadway debut that same year, appearing in Alexander Ostrovsky's Diary of a Scoundrel. Shortly after, he acted again on Broadway as an English soldier in Shaw's Saint Joan, with Siobhán McKenna. In 1972 he was acclaimed for his performance as a frustrated, unemployed New Yorker in Neil Simon's comedy The Prisoner of Second Avenue. It would be his Broadway swan song, though he did play the lead role of Levine in a 1985 Chicago production of David Mamet's Glengarry Glenn Ross.
He made his film debut in "Wind Across the Everglades" in 1958, and thereafter played a series of gangsters in films such as "Murder, Inc.," "Pretty Boy Floyd" and "Pocketful of Miracles." He was nominated for Academy Awards for the first and the third.
Unusual for an actor, Mr. Falk's name had cachet in both commercial and avant garde circles. He was friends with auteur actor-director John Cassavetes, and appeared in six of his films: "Husbands" (1970), "Machine Gun McCain" (1969), "Mikey and Nicky" (1976), "Opening Night" (1977), "Big Trouble" (1986), and "A Woman Under the Influence" (1974).
Notable later roles included the comedy "The In-Laws," which paired him with Alan Arkin, and "Wings of Desire," the Wim Wenders film in which he played a version of himself, wandering about a Berlin peopled by unseen angels.
Mr. Falk returned to the New York stage to star in an Off-Broadway production of Arthur Miller's Mr. Peters' Connections in 1998.