I have had (though thankfully not often) nightmares which sent me leaping out of bed, or starting away from my pillow or covers. They are usually realistic ones which feature me sleeping, then something scary happening to me in or around my bed.
For example, I had one friday night. I'm not sure it was really a nightmare exactly, since I picture those as long-running and scarier, but it was a icky dream. I was sleeping on my futon, both in the dream and in real life, because my parents were guesting in my regular bed. Somebody (I don't know who, but I remember a hand) placed a couple of large creepy bugs right on my pillow. I jerked away, sat bolt upright in bed, looked for the bugs. I looked for the person.
Nobody was there, and nothing was amiss. There were no bugs, and it only took me a few moments to realize it had been a dream. It was only 4am, but at that point I was sitting up, adrenaline flowing. Also, there had been bugs on my pillow. Even though they weren't real, I couldn't just lie back down there and go to sleep.
I got up, had some cereal, did some reading, and eventually fell asleep again. But my occasional weird dreams like this always give me pause. Why would my brain betray me like that? It's one thing for my subconscious to exhibit its stress or concerns in some external environment, but why would it make my own bed, my warm and comfortable cocoon filled with pillows and teddy bears, a scary place to be? (Even my futon I had filled with my usual bedding and stuff, and I've had dreams like this take place in my regular bed as well.)
It annoys me. It's not a terrible thing, as dreams go, and it's not frequent... but I don't approve nevertheless. My brain should know better than to make my sleep-haven feel unsafe, especially since it is a safe place to be.