Unreal

In the beginning of the first level there is this scene where a door is closed. The player can hear somebody screaming in despair. From under the door's partial opening the player can see some flashes of light and hear gunfire. After a few seconds the doors opens and the player sees  the first alien and enemy run away. While this game is not about terror, this scene does a good job in immersing the player in an alien world where many many dangerous await in his or her journey to escape this strange world. This technique also works great to catch the player's attention and make them more interested in the next chapters.

F.E.A.R.

This game is about horror and they successfully accomplished it with scripted events. There are times where lamps shake a bit, a scream is heard, a body falls off the ceiling, windows shatter out of nowhere, scarecrows fly as the player reaches a corner, the player jumps in water just to experience an hallucination, a shadow passes by, etc. I unfortunately don't have experience with this and cannot provide any advice on how frequent those events should be, nor when they should happen.

Sonic 3 & Knuckles

When the player meets the first sub-boss there is an scripted event. An army of machines attacks the lush forest which serves as the first level. After bombarding it, the previously lush forest turns into a burning forest. This event explains the change in the environment from one level to the next.

In the game's second zone the same concept is applied. Once the player meets Knuckles, he smirks at the player and pushes a button that turns off the power in the whole level. Every light is now off. In here I'd comment that to turn off the power would literally turn off all moving platforms and other interactive objects in the level. But that would make the level impossible to traverse as everything would be offline. Sometimes ideas conflict with realism and concessions have to be made. In Sonic's case the game isn't about realism, making this lack of realism excusable.

Alan Wake

When Alan Wake is being ransomed he follows directions given by a kidnapper to an abandoned mine. Many scripted events take place. The old wooden catwalks are on the verge of collapsing, birds attack, rocks fall down and block the tunnel, Alan's wife screams, the supernatural entity attacks the player with trains or cuts down trees. Many many games have similar events such earth shaking, gas pipelines blowing out, cars crashing, characters running in despair, etc. In regards to physics there is a trade off between heavy computations and animators carrying out the burden by hand. If cars crashing or rocks falling down are animated such that it looks natural, it's often good enough. It can be argued that by having the processor handle the physics in realtime we are taking the burden off the animator's shoulders. A counter-argument is that the processing power required to do so is often unavailable and due to artistic reasons it may be desirable to have fine grain control over animations.

If you look at the cinema industry not everything is done by hand or by real physics simulations. I don't have the required knowledge to tell which way is best and often both are used in different scenarios.

Max Payne 2 and Bioshock Infinite

In Max Payne 2 there is a level where the player takes control of Mona and Max is trying to escape the construction site. The player has to help the A.I. controlled Max by sniping enemies from above. Another example is Elizabeth in Bioshock Infinite. She never engages in combat and is immune to damage, which prevents her for either hindering the player or dying. Her A.I. also never stands still in the player's path.

Bioshock

This game is another great example of scripted events done right. It's not a horror game, but it has some scary moments that really add a nice touch to it. (the screenshots are sorted accordingly)