Leonard Nimoy (1931-2015) as Spock
"Live long and prosper," was a Vulcan blessing, typically used when characters greet or depart. First used in the Star Trek episode "Amok Time" in 1967, it has been liberally used throughout the franchise ever since.
It is typically accompanied by the Vulcan Salute and returned with the blessing, "Peace and long life."
In the Vulcan language, "Live long and prosper," was pronounced "Dif tor heh smusma" (Star Trek: The Motion Picture).
Outside of the Star Trek universe, the phrase and Salute are often used among fans.