Erotomania is a delusion in which the affected person believes that another person, usually a stranger, high-status or famous person, is in love with them. It tends to show up a lot when dealing with stalkers.
Discouraging stalkers was one of the major reasons why the phrase "Speak Now or Forever Hold Your Peace" was removed from a majority of wedding liturgies. In that, said person would show up (undetected) and sit in the pews, waiting for the requisite line before speaking up (usually, to claim that the bride or groom (as appropriate) was "meant" for him/her); or bursting in just as the vows are to be recited and claiming that the bride/groom actually loves him/her.
Still, the "speak now" line remains present in some versions of marriage liturgies, as a requirement to make sure the wedding is legal. As such, the "speak now" line has been modified with something along the lines of "If anyone knows any legal reason that this marriage can't proceed, you must declare it now." Of course, a sufficiently devoted stalker will nonetheless take the opportunity.
A reported reason for Manson Family member Lynette "Squeaky" Fromme's attempt to assassinate President Gerald Ford was her belief that this would please Charles Manson.
Richard Farley's attempted courtship of Laura Black left much to be desired, like a lack of Ax-Crazy. This case culminated in the first anti-stalker laws in the US.
Actress Rebecca Schaeffer was murdered by obsessed fan Robert John Bardo. Bardo was also fixated for a time on pop music's teen queens of the late 1980s, Debbie Gibson and Tiffany, and prior to her death, teen U.S. ambassador Samantha Smith was an object of his desires.
This is one of the main reasons why actor Tim Curry was extremely reluctant to talk about his role as Dr. Frank N Furter for so many years (It's only recently that he's become somewhat more comfortable talking about it). He was growing increasingly distraught over all the crazed fans stalking him and going through his garbage.
Margaret Mary Ray, who was completely convinced that she was in a relationship with David Letterman, breaking into his home so many times that they were apparently on a first-name basis. She later came to believe that she was in love with Story Musgrove and began stalking him.
The singer and musician Enya has had this problem a number of times, and people have managed to break past security and get into her castle (yes, that's right, she lives in a castle). No harm has come to her from these people, but she's understandably creeped out by it.
Extremely common in teenage relationships, to the point that at least one state has enacted laws allowing teenagers to get restraining orders to stop this behavior.
Lisa "The Astronaut Stalker" Nowak. She stalked the girlfriend of a fellow astronaut she reputedly obsessed over. The two astronauts had had a romantic relationship prior to the incident, but he broke it off.
The Kids in the Hall actor Kevin McDonald had his own stalker for a while after his famous "Daddy Drank" sketch aired. 
Alec Baldwin has one allegedly in the form of Genevieve Sabourin.
Doug Walker's had his fair share, the scariest ones being those who found his house address and sent oh-so-charmingly-detailed threats of rape, death and mutilation.
Singer Anne Murray has been the victim of a persistent stalker, a farmer from Saskatchewan who has served jail time for harassing her.
This is a major problem for sports figures as well. German figure skater Katarina Witt was stalked by a man who sent over 60 letters within a year, all growing increasingly graphic with their descriptions of what he wanted to do to her. Even after he was finally arrested, he still insisted that he was only trying to make her love him.
In his last years, the Duke of Richelieu was relentlessly stalked by Désirée Clary. Everywhere he went, the Queen of Sweden was never far behind. This, combined to his natural nervousness and the pressure he had to withstand as Prime Minister might have been one of the causes of his premature death.