Kirk: You know Spock, I love baseball. When we get to Vulcan, will you tell me the guys' name on the team so when I go to see them I'll be able to know those fellows?
Spock: Of course, Captain, but you know, strange as it may seems, they give ball players nowadays very peculiar names, nick names, like "Dizzy Dean." Now on the Vulcan team we have Who's on first, What's on second, I Don't Know is on third --
Kirk: That's what I want to find out. I want you to tell me the names of the fellows on the team.
Spock: Yes Captain. As I said, Who's on first, What's on second, I Don't Know is on third --
Kirk: You know the fellows' names?
Spock: Affirmative.
Kirk: Well, then who's playin' first.
Spock: That is correct.
Kirk: I mean the fellow's name on first base.
Spock: Who.
Kirk: The fellow playin' first base for St. Louis.
Spock: Who.
Kirk: The guy on first base.
Spock: Who is on first.
Kirk: Well, what are you asking me for?
Spock: I made no inquisitive statement. I simply told you who is on first.
Kirk: I'm asking you -- who's on first?
Spock: Yes, that is the man's name.
Kirk: That's who's name?
The rest is here:
http://songweaver.com/tv/strek/whosonfirst.html