Red Faction and Red Faction II was good for this also. In one of these games single player, I remember that I needed some key card to get through a door but I didn't have it. So I just put a satchel charge on the wall and then make my own door! The multiplayer in Red Faction had fully destructible environments also (Never played MP in RFII) so by the end of a long match there could be nowhere to hide, even if no one was using the rail gun.
Another fun thing you can do in *some* games is have interactive cutscenes. Games where the cutscenes are triggered by you walking to a specific point, and then it is rendered in-engine.
In Deus Ex, you can pick up items and move them. Like plants or boxes or whatever. If you pick up an item and walk into a cutscene trigger, the item will drop to the ground but will then be in the cut-scene. It is possible to have a scene where you are talking to an NPC, but there is a large plant between the two of you.
In Soldier of Fortune II, the NPCs are rendered in the game world prior to triggering the cut-scene. It is usually the case that you cannot see the NPCs first, as cut-scenes are often triggered by entering a doorway to go into a room, or turn a corner. Because the NPCs already exist in the game, and they have normal hitpoints, it means they can be killed. If the NPC is killed, the cut-scene happens as normal, except the NPC will be dead as a body, or their body moved out of the scene. The dialog still happens even if the NPC has died. The easiest way to accomplish this is to throw a grenade into the room prior to entering and triggering the cut-scene. Because of this behaviour, it is my theory that it is possible to kill Saddam Hussein who also see in the game. He is rendered in a level, in an open area where it should be possible to kill him with a sniper rifle or the OICW, before his cut-scene occurs. I never was able to get the timing down to get this to happen.
Recently (just two days ago) I found a type of "unintended consequence" in Battlefield 4. There is a part where you have to cross an open area and kill maybe a dozen guys and there is one tank to destroy. The exit to the next area is an archway that has concrete barriers about, and there is a truck (that you can't drive) next to the ammo crate. I am quite certain that you are supposed to go through this area on foot. However there is an empty tank in the open area you can drive. And if you try hard enough, you can get that truck to move out of the way and complete the next area in the safety of the tank.
