Stiff man puttin’ my mind in jail
Judge bangs his gavel, and he says “No bail!”
Gonna lick his hands, gonna wag my tail . . .
I … AM … KIROK!
and my little indian princess, Miramani
Garak: Doctor, I don’t understand why you’re making these accusations. Everything I’ve told you has been the truth.
Bashir: Even the lies?
Garak: Especially the lies.
No, sir, I shall not withdraw a single charge that I have made. You are NOT Captain Kirk. You have ruthlessly appropriated his body, but the life entity within you is not that of Captain Kirk. You do NOT belong in charge of the Enterprise, and I shall do everything in my power against you.
One of my favorite Star Trek lines actually came from an SNL skit:
“Bones, we need your help, this woman is choking to death!”
“Dammit, Jim! I’m a doctor, not a… oh, right.”
But then he was a very strange small boy.
Is that how you get girls to like you - by bribing them?
Bonk! Bonk! On the Head! Bonk! Bonk!
Captain, I must protest. I am NOT a Merry Man!
Shut up, Spock, we’re rescuing you!
“That which you call Ee’d Plebnista was not written for the chiefs or the kings or the warriors or the rich and powerful, but for all the people!..These words and the words that follow were not written only for the Yangs, but for the Kohms as well!..They must apply to everyone or they mean nothing!”
The universe is a spheroid region 705 meters in diameter.
“What is it with you, anyway?”
“some kind of star trek?” 
“There’s a way out of any cage, I’ll find it!”
“Space, the final* frontier”
*Said by Patrick Stewart, who put most emphasis on the “Cos we’ve gotten rid of bigotry you morons”.
Gentlemen, I suggest you beam me aboard.
You, you must be almost 30… have you ever kissed a girl?
You have to learn why things work on a starship…
“I will feed him.”
Dr. McCoy: Do you know what you get if you feed a tribble too much?
Capt. Kirk: A fat tribble.
Dr. McCoy: No. You get a whole bunch of hungry little tribbles.
Capt. Kirk: Well, Bones, all I can suggest… is you open up a maternity ward.