Basic Trope: A character stalks a person he/she loves.
Straight: Alice loves Bob, so she follows him, hoping for him to one day love her.
Exaggerated: Alice is a Yandere, and has followed Bob since grade school.
Downplayed: Alice occasionally watches Bob whenever they happen to be in the same place at the same time, but she doesn't deliberately follow him, and her feelings toward him are more like mild infatuation than an overobsessive crush.
Alice is a teenager who just can't muster up the courage to actually talk to Bob.
Alice is watching Bob to try and protect him from the resident Big Bad out of love.
Alice has literally No Social Skills. She can't even talk to Bob, let alone know that stalking is inappropriate and creepy.
Alice is a crazy yandere who wants to know what Bob is doing all the time.
Alice has cripplingly low self-of-esteem and thinks that this is the closest she'll get to being Bob's girlfriend.
Alice was hired to find some dirt on him by spying on him and it turns out he's really not that bad of a guy. But she is aware that if he know she was stalking him, he'd be freaked out. So she doesn't bother asking him out, but still wants to get to know him better. So she keeps to stalking even though it just makes the idea of her dating Bob more improbable.
Alice has stalked Bob all her life, at the same time Bob starts stalking a different girl and instantly gets shunned for it, as a stab at the Double Standards of this trope.
Alice and Bob are stalking each other, and end up sitting still for hours wondering why the other hasn't moved or put down his or her binoculars.
Alice follows Bob around in the most unsubtle way possible. Bob thinks it's all a string of coincidences that have them winding up in the same place over and over.
Zig Zagged: Bob and Alice managed to stalk each other. But it turns out they were both spies of opposite organizations, meant to keep tabs on each other, using love as a ploy. When their cover starts to slip, they both start Becoming the Mask and falling in love with each other for real, but it tuns out they were both just faking that and they're really not in love with each other at all, without the other one knowing.
Bob starts to miss Alice's stalkerish ways, even if they were a bit creepy.
Alice realizes that a distant, one-sided relationship is no match for a genuine one. The extensive familiarity she has with Bob's life and daily routine gives her the confidence to approach him normally, and they form a happy relationship, although Alice carries guilt forever.
Played For Laughs: Alice knows everything about Bob, his family, his favorite food, what color underwear he wears, and even his routine for getting up in the morning. And she can recite all of it from memory.
Played For Drama:
Alice is stalking Bob, who has known for some time and has actually taken quite a shine to her. But his brother Charlie, who knows nothing of the situation, discovers her stalking him and attacks, killing her in the process. Bob, not realizing who did it, vows revenge for Alice...
Alice is creepily obsessive, and not in a funny way.