This happened to me when I lived in Los Angeles a couple of years ago.
I worked at a club, so I usually got home at around 2:30 in the morning. I was dead to the world until ten or eleven am. I woke up suddenly, not from a dream or anything in particular, to find a haggard old woman floating about three feet above me. She looked angry, and she was entirely white, although possibly a little transparent, it's difficult to remember. I started screaming, and my boyfriend at the time, Andrej, put his arm around me and told me it wasn't real. He tried to comfort me, half asleep, into going back to bed. When I looked at the clock on our dresser, it was around 6:00 am.
Thoroughly freaked out, I eventually curled up next to him and went back to sleep.
In general, I am a very logical person. I always try to find a scientific reason for odd occurrences, and ninety-nine percent of the time, I do. However, I can't find any 'logical' reason for this occurrence. I wasn't trying to wake up from a nightmare, the room wasn't hot (I always wake up when I'm too warm, as I'm sure most people do). There were no loud noises to startle me out of my sleep, nor did I need to get up to use the restroom. I should add that I have no history of sleep paralysis.
I've read about old hag phenomena before, and this, to me, sounds like a textbook example. As long as I lived in that apartment though, I never had any other odd happenings occur to me while living there.