The first one I thought of was the "Nemesis" from the Resident Evil game of the same name. Before that though Resident Evil 2 prototyped the concept with the "Mr. X" enemy type. Going way back there were "Snoopers" in the Macintosh home computer game Colony, as well as "The Ship's Defender" in the early CD-ROM game Iron Helix. Pretty much the entire Clock Tower series is based around these kinds of foes. The puzzle/RPG Ao Oni is an indie video game that also likes to terrorize players with a relentlessly reoccurring...well, as the title says in Japanese - "Blue Demon."
I can't say I'm particularly fond of this game mechanic. Much like "It Follows," knowing that you are constantly being hunted can get pretty stressful. Even if the intention is to create an intense gameplay experience, such as in the case of Alien: Isolation, I know a non-trivial number of people who don't like having to endure that kind of constant anxiety (vicariously).
Something else I see people do is make questionable assumptions based on what they already know; usually with the intended goal of showing off how much smarter they are than the characters in the film (and possibly the scriptwriter). Before curling up into a ball of smug intellectual superiority though, I think it's best to consider how one got to that place. Thinking you're a badass at competitive online games while using hacks, is just asking for a lesson in humility. One of the creators behind "It Follows" mentioned in an interview that he was considering the idea of making a sequel if only to show how misunderstanding the rules through flimsy reasoning could lead to some disastrous consequences. I doubt it will ever happen though because that's exactly the kind of thing that would piss off a certain subset of the audience the same way cheaters get pissed and complain on official message boards after they get busted.
One last game I want to mention is Miasmata. The player takes the role of a shipwrecked survivor, washed up on the shores of a once inhabited (but now deserted) island. They are alone except for the presence of some small animals and one large predatory beast. This creature appears frequently, particularly toward the latter half of the game. Consulting the wiki reveals a large amount of information about the monster's behavior, as well as methods for dealing with it. However, the webpage article makes it clear that most of this info is based on what players have discovered through experimentation and as such remains unconfirmed by the developers as to its accuracy.