But the 77-year-old actor, who lost his right eye to cancer at the age of 3, has worn plenty of other disguises over the years, on the big screen, the tube and the stage.
His latest role is in comedian Paul Reiser's "The Thing About My Folks," (search) a part that Reiser -- although thinking about his own pop -- wrote specifically for Falk.
As Sam Kleinman, Falk's a loveable collection of neuroses and bluster, wrapped in a cloud of talcum powder.
He arrives at the Manhattan apartment of his son Ben (Reiser) with the news that his wife has left him -- and father and son embark on a road trip that yields surprising insights for both.
What did you think when you found out Paul had written this part with you in mind?
He didn't tell me that when he sent me the script -- he's a classy guy; he didn't want to put any pressure on me.
He went to visit his father, and his father was watching television, and I came on, and his father started to chuckle. So he's watching his father chuckling at me, and it occurs to him that I should play the part of his father.
I can't think of another job I ever got that had such a delightful origin. I mean, I never got hired because the author had a fond memory of seeing his father watching me on television. That tickles me.
Did you see anything of yourself in this character?
When I see a part that I can score in, I don't care how much it's like myself. I care whether I like the guy. And I do like him. A lot, as a matter of fact.
You've been to some film festivals where the movie has been shown. How are audiences reacting?
Every screening, some woman gets up and says, "I want my husband to see this movie." But what you're not prepared for is the emotional wallop at the end of it. The ushers come in with mops; everybody's bawling away.
Your banter with Paul seems very natural. Was any of it ad-libbed?
The fishing scene was the only one that was improvised, and that's because before we started the scene, I had the props in my hand, and I couldn't understand them. I was asking Paul all these questions, like, "Where does the hook go?" And somewhere around there the director said, "Just turn on the camera!"
The movie starts with you naked, covering yourself in talc. When was the last time you did a nude scene?
I think this was my first! It's a charming scene; it's delightful. I thought it was beautifully done.
There's talk of a possible Oscar nomination for this role. Will you worry about making another gaffe like in 1961 where you stood up when Peter Ustinov won?
[Laughs] Well actually, the next year I got nominated, too -- but there was no other nominee whose name was Peter, so I was spared that embarrassing moment. If there's another nomination, I'll worry about it then.
Did losing your eye ever hold you back as an actor?
No. I was amazed that anybody even noticed it. But my first agent said to me, "Well, you won't be able to do TV or movies."
That sounds like a big setback.
Well, you have to go back in time to whatever year that was, 1955 or something. All my acting had been onstage, so when he said that, I thought, "Who ever thought of doing TV or movies?"
Which role changed your mind?
You don't change your mind -- something comes along, and you take whatever comes along. You get going, and you just go with the flow. When I became an actor, I didn't even own a television set.
Ever get tired of being Columbo?
Oh, no. He tickles me. I love playing Columbo -- he's one of the richest characters of all time! You get laughs; you keep people's interest. No actor could get tired of doing that.