Happily, Quantum Conundrum brings up another topic I've been holding in reserve for a while, and that's jumping puzzles in first person games. I'm fairly sure we were all clear on this matter circa 2000 but apparently Quantum Conundrum was out back smoking at the time. Precision platforming in first person games just doesn't bloody work. It especially doesn't work when the platforms are small and, at the same time, being manipulated by a slightly unreliable physics engine.
First person can effectively give a game a certain atmosphere, from a story perspective. It can make a game more immersive or emphasize the everyman nature of a silent protagonist. But whatever game you're making, a first person perspective has to be compatible with what the gameplay is focused on.
There's a reason why your brain will unconsciously attach the word "shooter" after the words "first person", because that's where it works best. When gameplay is based around acquiring an accurate line of sight, as it is in shooters, first person is ideal. In a game like Half-Life 2, even the crowbar functions essentially like a gun, albeit an incredibly short-range one; you point and you click. The important aspect of a shooter, the thing which the camera is focused on 100% of the time, is the thing that the player is targeting.
Precision platforming, contrarily, is gameplay based entirely around knowing where the player is, spatially. Mario's always got his eyes on the flagpole at the end of the level but you won't actually see it 'til you get there, because what matters is that his big Italian winklepickers land on the platforms and not the spiky beetle things. In a first person game, the exact spatial positioning of your body is something you can never be sure of, besides the positioning of your eyes. Your feet could be literally anywhere within a rectangular area of floor that begins where your field of vision ends. My housemate was playing Deus Ex: Human Revolution a while back and he got stuck early on at that one point in the first hub city where you have to jump from one fire escape to another to infiltrate an apartment building. I had to point out to him that the secret was to jump a moment after you think you need to jump, 'cos the ledge you're jumping off disappears from sight about half a second before your feet actually leave it.
You will never see a bullet hell shooter with a first person perspective, because the one piece of advice that works for all bullet hell shooters is to focus on yourself, not your target. You're going to be spraying fire everywhere anyway and accuracy doesn't matter so much as navigating a maze of projectiles. Melee-focused games tend to be third-person, too, because again, the most important thing is where the player is. Hopefully, the player is not surrounded by angry bastards, about to get their bum bitten off by a canny sod behind and to the left of them. This is what I didn't like about Dead Island having a first person perspective.