The term stalker
characterises one who has an intense voyeuristic
obsession with a particular person. This obsession leads them to physically follow a person from place to place and observe them.
Stalkers most commonly attempt to remain hidden from their victims.
Stalker is also a film by Andrei Tarkovsky. See Stalker (movie).
Stalkers are also the protagonists of The Whispering Vault roleplaying game.