I don't believe in reincarnation, or past lives. But I don't disbelieve, either. As with many things paranormal, I remain a healthy agnostic. However, I have a personal experience from years ago that makes me take it more seriously than I take other paranormal subjects.
When I was kid, until about the age of 10 or 11, I used to have recurring experiences where I would feel as if I was falling. It was always the same - I could literally feel the air rush around me, and that feeling in your stomach that comes when you're falling. These experiences wouldn't last long, and they always happened when I was awake - often when I was lying down reading, but not always. Anyway, I've always wondered whether this might have been some "echo" from a past life, where I had experienced a traumatic fall, perhaps even a deadly one.
Perhaps those experiences, if there is indeed such a thing as reincarnation, follow us through into the next life, at least for a while. This might explain why the experience came to me as a child, but eventually faded away and then stopped altogether. Maybe as you grown into the new life you've been given, you slowly lose touch with the old one. But in those early years, the echos remain, at least for a while.
Like I said, I don't believe, because the logical skeptic in me could never base any conclusions on childhood experiences that happened decades ago. But as with politics, where it's always local, so too with the paranomral - it's almost always the personal experience that makes one wonder the most.
Incidentally, I have always had, and continue to have to this day, a fear of heights.