When my son was a baby, from newborn to 8 months old, we lived in a small apartment in an old building. He must have been about 7 months old or so when this happened. In the past year we had lived there, I had woken up to the sight of a human shaped transparent white ... thing... standing at the end of the bed, and then it would drift away toward the wall as soon as it "realized" I was awake. I assume. All these times I see it, I don't want to make a big deal because pregnant women are crazy and have crazy dreams, etc. Same with sleep-deprived new parents.
Until one night, I wake up to my son cooing, and he's pointing at the white figure. He and I both clearly saw it, though of course he couldn't say anything. That's when I was fairly sure I wasn't just seeing things. When we moved to a different apartment in the same building soon after that (there was a leak that needed to be fixed), I suddenly found that I was no longer afraid of using the bathroom in the dark. In the apartment with the white figure, the bathroom mirror gave me that heart-racing scared-of-the-dark feeling, and I just assumed I was afraid of mirrors in the dark in general. But when we moved, no problems with that. Also no more figure watching us sleep.
My son freaking loves this story now. He wishes he could remember it.