I saw some people had mentioned this in the ghosts thread but think it deserves its own because it is such a bizarre phenomenon and it would be interesting to hear other people's experiences.
I have had it about 5 or 6 times in my life, but I don't know many people it has happened too at all. The first time it happened I remember being completely terrified that I was going to remain permanently paralysed, which is an idea that generally scares me anyway (particularly since I worked with people with severe brain damage who were in permanent vegetative states or had could only move their eyes or a couple of fingers etc.)
It gets easier now because I know my body will gradually wake up after about 30 seconds, but it is very hard not to panic and start hyperventilating.
I have never felt a "presence" simultaneously but this is meant to be what a lot of alien abduction stories are attributed to.