"There can be only one" is the belief and motto among the immortals in the original Highlander film, its sequels and spin-offs. It implies that all immortals must fight and kill one another until only one remains standing; this "one" shall receive The Prize.
Connor MacLeod first heard these words from The Kurgan in the battle between Clan MacLeod and Clan Fraser when The Kurgan impaled him and was about to cut his head off. Connor was saved by his clansmen, who rushed up and stopped The Kurgan.
Ramirez learnt of Connor MacLeod's "miraculous" survival, and tracked him down. He taught MacLeod everything about the immortals and the Quickening. He revealed that when only a few of them were left, they would irresistibly be pulled to The Gathering in a faraway land and fight for The Prize. He summed up by saying, "In the end, there can be only one." MacLeod was also told that an immortal was safe only on holy ground, and that immortals could not have children.
In his search for the Highlander, The Kurgan met Ramirez in MacLeod's home instead. He overpowered Ramirez after a hard battle, and also repeated the phrase before beheading Ramirez.
In 1985 New York City, Brenda Wyatt was suspicious of MacLeod and she was following him when The Kurgan appeared and attacked MacLeod on the street. The Kurgan taunted him with those words once again during the fight. They broke off and escaped when a police helicopter arrived. Brenda asked MacLeod what the phrase meant, but he bade her never to follow him again.
MacLeod faced off The Kurgan one last time. After beheading his opponent, he finally exclaimed, "There can be only one."
A Kind of Magic
"There can be only one" is also part of the lyrics in Queen song "A Kind of Magic" which is the closing theme music during Highlander's closing credits.
Highlander: The Search for Vengeance (2007)
In the animated film, in Rome, during the year 476 Marcus Octavius said "There can be only one" when he tried to behead Colin MacLeod. He didn't care about The Game. Marcus apparently always said this when he killed another immortal.