Stalwart, who has a severe crush on Nikki Reilly (Fey) in the Whateley Universe. He declares his love for her in front of the whole Quad and Nikki's dad, completely embarrassing her. She throws him across the Quad. Then later, the only reason Nikki survives an attack by a superpowered ninja assassin-slash-rapist is because Stalwart's been stalking her. Since he almost dies trying to save her, she cuts him a lot of slack. They're currently dating. Fanon thinks she can do a lot better.
Worm: Dragon has a habit of hacking into the video and audio feeds in Armsmaster's apartment when he isn't paying attention. Granted, this was before she realized that she had feelings for him, and after their Relationship Upgrade, she's a lot less discreet about the constant surveillance. Armsmaster, for his part, doesn't really seem to mind.
An odd variation (a non-villain example), from Survival of the Fittest is Matthew Wittany, V3's resident Woobie. A fan of photography, he carried around an album filled with pictures of boys he found attractive. Anderson Walker, the subject of most of these pictures, was not best pleased when he discovered this. Neither was his boyfriend, Sean O'Cann.
Exemplified in thisYouTube parody of "So Happy Together".
Billy, the titular character from Dr. Horrible's Sing-Along Blog follows Penny and Captain Hammer around in a series of strangely effective disguises, including a mobile bush and, in a hard to notice instance, posing as a worker in a homeless shelter, complete with a blatantly fake mustache. However, there's some argument as to how stalkery he is.
Zaboo in The Guild, who has mistaken Codex/Cyd's online flirting for a relationship and shows up at her house unannounced. He also memorizes the floorplans of all her residences (past and present) and photoshops a picture of the two of them using her DMV photo. (Codex, interestingly, is played by Felicia Day, who was also the stalkee in the aforementioned Dr. Horrible.)
Amiright has a darnright creepy example in the form of a parodist named Andria, who goes beyond creepy and into Nightmare Fuel terrority.
Amir from College Humor's Jake and Amir. He knows Jake's weight (both when he wakes up and right before he goes to sleep), has an account of every outfit he has ever worn, knows his mother's middle name (but can't spell), knows his password on facebook even though he changes it every day, knows what criminal activity he did on March 15, 1999, and much more.
Alex of Awkward. is this toward Lester; being housemates makes the stalking part that much easier.
The Nostalgia Chick towards Nella, especially seeing as how she has cameras that have a clear view of both the woman's bed and shower...
Weebl's cartoon Anything:I, I broke into your room! I hope you don't mind, you probably do! And it keeps getting worse from there.
The Joker Blogs - the title character for a certain Doctor Harleen Quinzel. He leaves a corpse in her office as a "present" and escapes from Arkham so he can murder her fiance during the wedding. The worst part is that she's still working at Arkham when he's recaptured at the end of the series, claiming that leaving would just be "letting him win".
Played for comedy in episode 5 of Echo Chamber's "Trope Of The Week": Zack starts acting this way toward Dana, following her around with his camera all day before saying he loves her. She responds by exhaustedly closing the door in his face.
Cecil of Welcome to Night Vale comes across as this at times towards his crush, Carlos. For a while it seems as though Carlos is uninterested, and perhaps a little put off, given Cecil's tendency to go into Purple Prose rants about Carlos's perfect hair on the radio, but eventually Carlos changes his mind, and asks Cecil out. They've been dating since episode 27.
Rather Vocalized Illusion has LylSweetsFairy, a very vocal and energetic fan who usually comments on how "cute" or "awesome" Bhaalspawn is. The show's creator takes this in stride, and has stated he finds it cute and flattering.
Paul in Website/Chatoyant College followed Corrie to Chatoyant College because he's Not Good with Rejection. Some acquaintances of Corrie try to help by subjecting Paul to a magical restraining order. However, Corrie feels that magic should not be used to subvert someone's will so rescinds the order in Book 9. See If I Can't Have You....
A series of threads on 2ch recounted the (supposedly true) story of a boy who simply could not comprehend that his crush did not like him back. It started with him sending her 600 emails and went downhill from there.