If the protagonist has powers then the classic "spider-man losing his powers" moment would force the player to explore more unique ways of staying alive. Doing this just as the player is getting comfortable and even cocky with the game mechanics is a perfect way to build tension, change pacing and give this character a sense of fragility, reminding the player of their character's humanity. Its the moment when the hero seems beaten that the audience will care about them the most. You'll have to rely on your game's story and character design to best choose how to achieve this.

You could also try giving the character someone they care about to protect. This is probably harder in a chase scenario.

Rules of a roller coaster are that by making the path narrower the ride seems faster. Just like the classic helicopter game. The farther you get the more narrow the path becomes and the faster and more tense the game feels.

Cheers guys, all good ideas. I've already incorporated one of them in the design. Thanks a lot for your help.

Not sure if you're still soliciting ideas but I love the classic Uncharted trick whereby the camera faces backwards instead of forwards in the chase scene. Meaning its placed directly in front of you and staring at you and the background, so you can't really see where you're going and you can see whoever is chasing you gain/lose distance. I guess obstacles could be added if you pulled the camera further forwards making the player appear somewhere in the middle of the scene (to give them enough time to adjust to oncoming obstacles).

I felt so tense just running away from the crumbling floor/vehicle/enemy and really it reinforced my belief that Naughty Dog is just plain awesome.

Not sure if you're still soliciting ideas but I love the classic Uncharted trick whereby the camera faces backwards instead of forwards in the chase scene. Meaning its placed directly in front of you and staring at you and the background, so you can't really see where you're going and you can see whoever is chasing you gain/lose distance. I guess obstacles could be added if you pulled the camera further forwards making the player appear somewhere in the middle of the scene (to give them enough time to adjust to oncoming obstacles).

I felt so tense just running away from the crumbling floor/vehicle/enemy and really it reinforced my belief that Naughty Dog is just plain awesome.

That's superb. Uncertainty is the mother of tension.