It happens to me quite a lot but only after I've woken up and then gone back to sleep, or at least that's the only time I remember it happening.
I don't know if that's a typical thing or it's just me but during that half awake/half asleep dozing stage before you drift back off I quite often start to daydream and then when I fall back to sleep properly, it's a lucid dream - I know it's a dream and I'm guiding it along so I can change things but it's a real dream and sort of effortless and automatic. They are really pretty cool and much more vivid than a typical idle daydream, actually had an interesting one this morning as it happens.
Another thing that happens to me quite often in the morning is dreaming that I've gotten up already and am doing all the normal, mundane morning things only for me to realise that I'm still asleep and then wake up later than I had wanted. It's like my mind is trying to trick my body into getting more sleep. Quite annoying.
