Best line of his IMHO was in Out of the Past (1947) Kirk Douglas as a crime kingpin with some toughs tries to recruit Mitchum down in Mexico in his hotel room and Mitchum replies
Let’s go down to the bar. We can cool off while we try to impress each other.
There are so many, but I like this one from Macao:
“You’re going to have to get used to me dripping wet from the shower.”
More here:
http://home.sprintmail.com/~sknolle/mitchum/quotes.html
Great scene! And that film is the granddaddy of the noir genre.