I’m thinking of Woody Harrelson in No Country for Old Men.
Orson Welles’ performance in The Third Man (1949) lasts about five minutes, yet indelibly etched his public persona (and musical theme) for years before obesity and shilling for cheap wine replaced it. His “cuckoo clock” speech from the film has also entered the pop cultural collective unconscious.
Influential? Well, how about a guy who tosses out a frequently quoted line like: “What we have here…is a failure…to communicate.” (Strother Martin-Cool Hand Luke)
Joe Mantell as the guy who says “Forget it, Jake, it’s Chinatown.”
Probably not what the OP had in mind, but this thread got me thinking about Bronson Pinchot, playing Serge from Beverly Hills Cop. ‘It’s good, you should try it.’
Well I don’t know about influential as such but that’s a good call for sheer scene-stealing (that’s easier to type than to say)
Along the same lines what about “Johnny” in Airplane! but again perhaps that’s scene-stealing rather than influence.
I think that you could perhaps just do a trawl of Tarantino and Coen Brothers movies and come up with a bucketload of minor but influential characters.
(Jesus from The Big Lebowski is a very good call)
I immediately thought of James MacArthur as Ensign Ralston in The Bedford Incident. He’s present on the bridge throughout most of the movie, but it’s still a pretty minor role…until he hears “But if he fires one, I’ll fire one.”
Nitpick: The article “a” was not in the line.
https://www.researchgate.net/publication/294100032_What_we've_got_here_is_Failure_to_communicate
“Lucille” the car washing tease in Cool Hand Luke: “She knows exactly what she’s doing.” It sets up the confrontation between Luke and Dragline (George Kennedy) when Luke tells Dragline to stop talking about her at bedtime. Dragline then essentially sets up the boxing match for the next day where Luke doesn’t back down, earning Dragline’s respect for the rest of the movie.