This actually happened to my mom when she was little. She doesn't want to post this herself, but I think it's interesting and spooky enough to make public.
When my mom, "Liz", was about 12 years old, she and her mother were living in an old farmhouse in Missouri that had no inside plumbing and no close neighbors. Her mother had told her about some strange happenings, but nothing had ever happened to Liz.
Liz was afraid of the dark and one night she asked to get in her mother's bed. As Liz was trying to drift off to sleep, she felt something jump up on the foot of the bed. Having no pets, and not being able to see the thing because of the dark, she quickly became frightened. She said it felt like it was about the size of a house cat, but was extremely heavy. The thing started moving up closer to her. She reached for the string that was connected to a bare light bulb. When she turned on the light, there was nothing there. When she turned the light off again, the thing immediately started crawling up the bed towards her. She kicked at it and it fell to the wooden floor with a heavy thump, and then immediately jumped back on the bed. It started moving towards her again, again she kicked it off, and again it jumped back up. That time, she let it come closer. It came up to about her chest. She then realized that it could possibly do her harm, but she couldn't get it off because of it's weight. Thinking it was just her imagination or some animal that had gotten in the house, she flipped the sheets over it, and put her arms on top of it. She felt a form, soft like a rabbit, but extremely heavy, and cold. She got the strength to knock it down once more. That time it didn't come back.
Liz woke up her mother and explained what had happened. Her mother said she had experienced the same thing before. Neither one ever experienced the thing again.