Played perfectly straight in Sherlock Holmes: The Awakened and Sherlock Holmes: Nemesis, possibly as way to avoid programming pathfinding AI. As long as you are looking at Watson, he never moves. You can walk as far away from him as you want, and he will stay in that spot. As soon as you turn around and turn back, however, he will be right next to you immediately. This leads to some cases where you can walk up to a door, turn away from Watson, open the door, and find him in the room, despite it having no other entrances.
Partially averted, however, in the remastered version of The Awakened. This time, you can see Watson running to keep up with Holmes.
The developer was completely aware of the amusing creepiness of it, and just ran with it in an April Fools video for Crimes and Punishments.
Played absurdly straight to the point of on-screen teleportation in Final Fantasy Tactics, where upon being defeated in battle important NPCs will literally teleport away from the battle whenever convenient, even if such a power makes no sense for them, or you acquire them later, at which point they lose their plot-driven abilities.
This trope is a common means of news conveyance in classic Final Fantasy games. Journey long distances over treacherous terrain from Town A to Town B, and somehow the residents of Town B have already heard the news about Town A, even though no one could have possibly made the journey faster than your party did. (Perhaps someone Took a Shortcut? Or your party just got bogged down in all those Random Encounters?)
One commentator described the appearance of this tendency in video games as "NPC powers", noting the ability of minor characters in Resident Evil to appear on the other side of locked doors, survive alone with only a handgun for defense, and mysteriously beat you to any location you're traveling towards.
Somewhat justified in Resident Evil 2, with Sherry. A close examination of the rooms you see her disappear into or from will show some vent or opening that the character will note is "too small for an adult."
Doesn't quite explain how she got into the chief's quarters when the corridor was blocked by the helicopter debris.
Bitores Mendez in RE 4 pulls this just before his boss fight, when the camera shifts to face Leon.
In Resident Evil 3: Nemesis, Nikolai is sometimes present, depending on the player's path, at the gas station when it catches fire and explodes, yet still shows up unscathed later.
In RE 4 the Merchant at one point appears in a room adjacent to one he was already in, despite not passing Leon.
Randomly placed enemies in Baldur's Gate pop up practically anywhere the "fog of war" covers, never appearing in areas you can see (unless you load a saved game, in which case some can even appear out of nowhere when it loads!). A particularly absurd example would be the hordes of Kobold Commandos that almost seem to pour out of the very walls in the Firewine Ruins.
Chronos from One Must Fall 2097 has a similar power, with the in-game explanation being that it's a Humongous Mecha designed for time-critical spaceship rescues.
Reimu has an ability very similar to this in Subterranean Animism, the eleventh Touhou game, when she has Yukari helping her. Minus the punching, since this is a SHUMP and all that. This ability was later given to Yukari in a patch of Scarlet Weather Rhapsody. Still minus the punching, since it's still a defensive tactic.
Used regularly in BioShock, where Splicers will suddenly appear in areas that had been cleared out minutes before. Kind of justified in that Rapture is one giant city of crazies and new ones will inevitably wander in after Jack has passed.
There's also the Houdini Splicers. Justified in that they also have on-screen teleportation.
F.E.A.R. makes use of this with Alma and Fettel sometimes appearing without warning when the Point man turns around. In their case, though, its quite justified in that both of them are using psychic projections or hallucinations.
In the game Myth 2, the Deceiver can travel much faster if he is unobserved.
Used as part of a game mechanic in Left 4 Dead - the Infected team in Versus can spawn anywhere, as long as there's no Survivor within 10 feet and with a line of sight to the spot. Also, if the Survivor team gets too far away, the Infected can Offscreen Teleport closer to their location.
The AI Director uses line of sight for all infected spawning, which can lead to hilarious instances where a massive horde of zombies pile out of a small bathroom. This can happen even if you had previously cleared the room, and in some instances, you can manage to be in an area when the infected begin spawning around you.
The Survivor bots do this if they get far enough behind you.
In Metal Gear Solid 3: Snake Eater, during your fight with The End, he can immediately appear right next to Snake if the player spends too long in first-person mode.
In Dementium: The Ward, you acquire your first gun by taking it from the body of some poor schmuck who fell prey to this. The first living person you come across has closed himself off in a tiny boiler room, which only has one door, and has been shooting the undead creatures as they come in. While he's busy threatening you with his gun, a zombie impossibly appears behind him, and kills him.
Used by Flying Fox in Heavenly Sword, though he uses it on another villain and is played for laughs due to Bohan's confusion.
Haunting Ground, arguably. Although the Big Bad gains genuine teleportation after going One-Winged Angel with some Applied Phlebotinum, the other antagonists (particularly the maidDaniella) already teleport almost constantly. For example, when Fiona finds Daniella tending the fire in one room, the player can go into the opposite identical room and find her hiding in the closet. Given how there is no way she could have gotten there without first passing Fiona in the corridor... yeah.
In Déjà Vu II: Lost in Las Vegas, The Dragon Stogie takes this to completely absurd levels, appearing out of nowhere no matter WHERE you happen to be at the time. Doesn't matter if you're on a train well on its way to Chicago, or out in the middle of the Vegas desert...
In just about every gorram racing game if you get too far ahead of the AI opponents, they'll magically teleport to just behind your tail.
In Half-Life this is the first major hint that the mysterious man in the suit is much more than just a regular Man In Black overseeing the military opperation at Black Mesa. He often is seen in the distance during firefights with aliens or soldiers, calmly going his way, often into rooms or side passages that turn out to be dead ends without any doors when you try to catch up with him.
The ending and particuarly Half-Life 2 make it clear that he is some kind of Alien in a Human Suit who does in fact have the ability to teleport between dimensions. Either by a device in his briefcase or as a natural ability.
There's an add-on for Garry's Mod called the "Harmless Companion Cube." Don't turn your back on it......
How exactly do the villains in Pokémon get away when the game decides to turn the lights out?
To be specific: The Trainer usually runs around in the background, along with his Pokemon. In stages where this isn't possible, he turns into a small ball of light and warps to the next available spot farther ahead when you're about halfway there. This is very easy to miss, especially in the middle of a fight.
Ally Example: Tricky from Star Fox Adventures. Run too far ahead of him? He's around the next corner. Had to climb to proceed? He'll catch up. He cannot teleport across large pits with flame jets and moving platforms for some reason, however.
The Grand Theft Auto games do this with the police and other authorities once you get above a two-star warning level. Essentially, there is no hiding spot inconvenient enough that the authorities can't magically appear to shoot at you, even when it should be impossible for them to even know where you are. IE, if you run out of their line of their sight for a long time and are holed up in say a small shack, they will still spawn close to you just out of your LOS.
Vice City was the worst offender, with the "supercop" that could spawn anywhere, even in an empty pool you were hiding in.
Game past IV averted it somewhat with the HUD showing the cops' line of sight. Still, you will often see a cop line of sight appear on your HUD in areas that it would make no logical sense for them to suddenly appear (any event triggered wanted level will do this as well).
Heavy Rain abuses this quite a bit. In a typical version of the warehouse scene, it will show the empty warehouse, you walk up to save ShaunNot Jason, and the killer appears right behind you. Then another character runs out of nowhere to save you. Also Manfred's killing, done without Lauren noticing, even though she's in the same room. Also Norman's ghost, although that one's justified by it being inside virtual reality.
In the first episode of Cool Game for Attractive People, Homestar Ruiner, Homestar will move into Strong Bad's house and lament the three problems that have crept into his life. As he does so, there are effectively three Homestars at once, implying that he's teleporting around when Strong Bad isn't looking. This gets a reaction shot when Strong Bad first notices.
Friendly example, though still incredibly creepy: In Kingdom Hearts II, your party members will warp inexplicably. Normally, they will just try to follow the path you took to reach any given spot. But, sometimes, you can get to areas that are plain and simply impossible for them to reach (some of the stores in Twilight Town, for example). Now they'll jump around like idiots so long as you're looking at them...but turn away...and they're right behind you. Bonus creepy points if you enter first person mode to do this, as when you turn back around you'll get a truly unnerving close-up.
They also do this in Days, however this may be more zig-zagged as it's usually a lot more common to see them teleport right in front of you.
In Assassin's Creed: Brotherhood, if you call your horse, it will appear somewhere nearby just out of sight and gallop to Ezio, even if you had left it behind far away. The Assassin recruits are also very good at this; if they are not running in from just out of sight, they are leaping out of hiding spots that they probably should not have been able to reach before you call for them.
Alternatively, they'll simply appear, complete with cool Animus 2.0 visual effects, giving the impression that they did actually teleport in.
In La-Mulana, when the Faceless Eye chases after Lemeza, no matter how quickly he gets to the next screen the eye is only a few seconds behind.
[Averted in the Wiiware/PC remake. The eye thing now stays where it is when you go across screens, and needs to catch up to you.
NetHack won't randomly spawn monsters in line-of-sight (unless there's no other option). If the player is unable to see monsters can spawn anywhere, even right next to the player. This occasionally surprises players who are blinded for a single turn.
Ghost Master lets you benefit from this—unlike humans, the ghosts you control don't take any time to move from room to room.
In Amy's levels of Sonic Adventure, Zero will sometimes suddenly reappear by smashing through a wall that he had no apparent means of getting behind.
Ran with in Rainbow Six: Vegas with the terrorists. In some rooms, you can call in the thermal scan and see a squad of terrorists appear out of thin air.
Same with Ghost Recon: Advanced Warfighter and Future Soldier, the latter even giving you handy magnetic goggles to let you see the new enemies spawn in.
In Super Mario RPG, Croco breaks into Bowser's Keep even with all access cut off. Toad makes it farther to the Final Boss Corridor despite being captured every few minutes by low-level enemies in one of the first areas of the game.
In Red Dead Redemption, you can be anywhere, even another country, where with one simple whistle your horse will be there.
True to form, the eponymous monster of Slender only moves when you're not looking. Unfortunately, staring at him for any length of time will drive your character mad, so it's hard to use this against him - especially late in the game when he can Jump Scare right in front of you. If you're facing him but can't actually see him due to an obstacle, you can keep him in place by walking backwards.
Necromorphs in Dead Space have Air Vent Teleportation. Particularly noticeable with the Hunter Necromorph, and especially in the scene where you finally get rid of it: you can clearly see the thing slowly crawl into the vent a good ten meters away from you, then instantly move to the vent right next to you, then slowly crawl out.
All Link's Animal Companions do this in The Legend of Zelda series. In the 3D ones when calling your horse, Epona, the camera usually makes an effort to pan in the direction you couldn't see only for her to be there running towards you. She can't teleport to places she can's naturally reach however. Maybe she's just faster than she lets on.
The bronze man of Kraven Manor moves about whenever you're not looking at it, and will try to strangle you if it gets close enough. He eventually foregos any and all subtlety, and demonstrates the ability to move whether you look at him or not.
Most humanoid bosses teleport, but they do it much more often if the camera is facing away from them (usually if you're running away), and usually from behind or to the sides.
The game usually spawns mooks only in places you aren't currently in, but it gets to this level when there's no other way they could have reached the room they appear in.
Just like in the film it's based on, the game for The Emperor's New Groove lampshades this during the City and Catacomb levels, where Pacha appears at the beginning and end of each, despite Kuzco (the player character) having to do many difficult tasks to get to the same spot. Pacha explains that he just takes shortcuts, causing Kuzco to ask him to tell him about the shortcuts next time.
Any Turtle not keeping up with the lead Turtle(s) in Teenage Mutant Ninja Turtles 2013 in the Fixed Camera will magically teleport next to you. This can lead to a bug where they WON'T due to you being in a tight space they can't fit, leaving you stuck and unable to move, or them not following you if they're blocked by a railing or other Insurmountable Waist High Fence but are still visible, leaving you unable to move forward until you go back to retrieve them.
Antichamber: Assume the environment around you will do this to you, and it becomes a lot easier to progress.
Five Nights at Freddy's: The animatronic puppets that stalk you seem to have been taught by Weeping Angels, with them even standing right outside your room and yet not attacking you. Just don't peek at the camera with them still there. And don't think the fourth, Foxy, will follow these rules, he'll just blatantly charge your door in full view of your camera, giving you only few seconds to shut the door if you spot him running.
The gargoyles in the horror dungeon game Dreadhalls follow similar rules - they sometimes turn their heads on camera, but only seem to move when you're not looking.