My biggest fear was actually in Harry Potter. Y'know that scene in Deathly Hallows where Harry is trying to reach the sword of Gryffindor in the frozen lake? Yeah, that. Just a ton of terrifying things mushed together in one horrific event... *shudders*
First off, being depended on. Knowing that your failure (in retrieving the sword) will result in not only disappointment on your part and others, but also in actual deaths. Lives hinging on your success. Just...awful.
Then the freezing cold water. Not exactly a phobia of mine, but it wouldn't exactly be pleasant, now would it?
Next, being so close to your goal, just inches away from the hilt of the sword, when the locket starts strangling you. I have this weird thing about my neck; I hate things/people touching it. I can't wear high-necked tops or necklaces that are too tight. The thought of being strangled or suffocating scares me to death. What an awful way to go... Oxygen is something that everyone takes for granted because it's this invisible thing that's always there. It is incredibly unlikely that you will ever face a situation where oxygen won't be available. And the thought that the most basic ability of inhaling said oxygen can be taken away so simply... Terrifying. Especially if the oxygen is there for grabs but you can't do a single thing about it...
Then we have drowning. Pretty much what I just said about suffocation and all that jazz. The thing about drowning that terrifies me is the simple lack of oxygen. Being unable to suppress your basic urge to simply breathe and being forced by your own body to swallow gallons of water in place of oxygen...
Then when Harry is thrashing about, the camera zooms out and shows that, on the surface, there's only a couple of bubbles penetrating the silence. Horrifying. He could have floated to the bottom of the lake, never to re-emerge, and no one would be any the wiser. To simply disappear and no one even notice your absence. Brrr...
Next, thumping on the ice, unable to find the hole you had entered from. Being so close to saving yourself from death, and something so silly as not being able to find the exit is ensuring your demise. Also, using the last bit of oxygen you have left in a feeble and futile attempt to escape your grave, or at least alert someone that simply isn't there to your plight. Just the desperation and the futility of it all... And the realisation that you are going to die and there is not a thing you can do about it. Also that you have, in fact, let everyone you have ever known/loved down. Not to mention the rest of the planet, really.
And finally, seeing someone walking on top of the ice that isn't helping you. (I know that it was Ron, and that he does in fact save Harry, but at that moment you wouldn't know, so...) In what you have come to realise as one of your last moments alive, you suddenly see someone that can help. The brief moment of ecstasy is short-lived, however, as you notice that they are simply walking on the ice, not trying to save you, or even acknowledge your existence. Again, the slightest chance you had at surviving is dashed and you realise that no one will even know of your death. Ugh, the whole thing was just horrible... :c
Maybe I'm just reading waaay too much into that scene, but I thought it was friggin' terrifying.
To sum up, my biggest fears are failure (especially when others are depending on me and their subsequent disappointment), being alone, being forgotten and suffocation.