I don't think you're alone, Olivant. I dream just about every night, yet if I don't make an effort to remember any of it (by thinking back to it and trying to recall what had happened, or perhaps by telling it to somebody), it's soon gone from my mind.

And more recently, I've had the same experience with dreaming just after quickly drifting off for a bit. I take about a ten minute nap each morning before leaving for school (instead of waking up later, which I'll admit sounds sort of silly), and I've actually had dreams during that time.