In college, right before I graduated, I lived in a house with a couple other people, but on this one particular night I was the only one home. Set up: Because I was going to be moving soon I had lots of boxes around my room. I also have a cat.
So I was alone in the house one night, already asleep when something wakes me and I hear a thump one of the boxes in my room. I just assumed it was the cat playing and started to drift back to sleep. Then I felt the cat on the bed next to me. She was crawling onto me. But as she kept crawling I started to think "this is too heavy to be my cat." So I opened my eyes and saw an arm across me. I turned my head and looked up into a face staring down at mine. My fight-of-flight instinct failed me and all I did was say "What the hell. Who are you?" And he/she calmly got up and walked out my bedroom door. I called the police but they didn't find anyone and weren't able to determine how someone got in.
Some people have suggested that it was a nightmare, but I know that it actually happened because I had to get out of bed to close bedroom door after he/she walked out, and I always slept with the door closed. To this day I can never be sure if this was a legit bedroom intruder or a ghost. But I never slept in that room again.