Tough one. A few favorites:
"It's wondrous--with treasures to satiate desires both subtle and gross--but it's not for the timid."-Q, speaking about exploration of deep space in TNG: "Q Who?"
"Resistance is futile."-Many voices of the Borg in TNG: "The Best of Both Worlds, Part I"
"We are not interested in your display of force."-Spock responding to Loskene's threat in TOS: "The Tholian Web"
"Vulcan, like Earth, had its aggressive colonising period—savage, even by Earth standards—and if Romulans retain this martial philosophy, then weakness is something we dare not show."-Spock on his people's lost brethren in TOS: "Balance of Terror"
"Risk is our business."-Kirk on the point of being in Starfleet in TOS: "Return to Tomorrow"
"Her five-year mission: to explore strange new worlds, to seek out new life and new civilizations, to boldly go where no man has gone before."-TOS Opening Credits