"Respect me for me," or "Respect my authority," both of which are demands for acknowledgment, recognition, consideration.

hey dude you better respect my mother else i will tear you a new one

Person 1; "Bitch, I want fucking respect."
Person 2; "It goes both ways."
Person 1; "Not in my book!"

Joe: Damn why was Sarah so pissed just now?
Mark: Yeah, Eli just No Respected her in the cheek.

person 1: you're a fag!
person 2: no you're a fag!
person 3: Stop it! don't you people have any respect for one another?
person 1 & 2: ... (to person 3) you're a fag.

Teacher: Johnny, it's time that you learned the meaning of respect!
Little Johnny: *goes to urbandictionary.*

1) If you don't respect me, I won't respect you.