I remember my dreams (a least a couple of them, anyway) every night. I’m surprised there aren’t more people who do this. They’re emotionally vivid, in color and I’ve died in them a number of times. As a matter of fact the emotional “hangover” from the unpleasant ones can last a couple of hours.
I’ve always felt, just from my experience, that my brain is spending that time collating the day’s events into long term memory. There are aspects of the dream that are from the day mixed in with lots of memories and images from the past. I imagine my operating system running through the day’s buffer and doing a tag search in long term storage.
One datum point, anyway…
I think someone already mentioned this but it is indeed possible to start remembering your dreams. Keep a notepad by your bed and the second you wake up start writing down your recollections. At first it may be only once a week or so that you remember something, but you will get better. Even if you claim you never remember your dreams I think you will be surprised that you do remember quite a bit, it just disappears really quickly after you wake up. Eventually you will get to the point that you no longer need the notepad.
If I’m in a boring lecture, but I’m fighting really hard to stay awake, I will fall asleep slowly enough to see what happens. As my head moves slowly down due to shutting down muscles, my vision blurs up and I become cross-eyed just before my eyelids shut.
Also, if you remember falling asleep in a loud place like a car, you will notice that there is a very sudden instant where you go “deaf” because your brain suddenly shuts out the outside world.
Also, a “LOL ME TOO” for Alex_Dubinsky who said your thoughts become vivid, bubbly and random.