Okay, since no one seems to want to start, I guess I'll break the ice for this thread.
My usual terror-filled nightmares feature a horrifying creature (strangely elongated limbs, morphed limbs or faces, etc.) that chase me, attack me, or kill me. What makes it horrifying is that I can see both what's happening first-person and what's happening in third-person and both versions are me. Another thing that gets me is when I cannot face off against the creature or I'm boxed in and cannot escape, because then it just leads to a chase that never ends well. Smells also play into the fears alot, with disgusting/overpowering scents rolled into the monsters themselves.
Another type of nightmare that I have had involves my body being torn apart or sliced up, and I'm able to poke and prod my own wounds. It's a VERY weird nightmare and sends shivers up and down my spine. While there is no pain, it still scares me to the point where I'll wake up in a cold sweat.
One strange nightmare that I've had which left me feeling oddly disturbed was when I had been replaced by someone and no one could tell the difference. It felt almost like an out-of-body experience dream thing, with no one able to see me, even as I tried my hardest to get people's attention. When my closest family and friends accepted her so quickly and easily as me, I tried yelling out "No!", and started to force myself to wake up. It felt like there were weights on my limbs as I tried to get up, which made me freak out (in my half-asleep state).
When I finally came to, I was befuddled by both my realization that it was only a dream and the remnants of my fear. I've never had the nightmare again, so I'm assuming the fear that inspired it has been mostly contained or soothed.