fukitol - Whether it is correctly dreaming or not I can vouch for the fact that this phenomenon does exist. I normally experience it as I am falling asleep so I get all the images and whatnot you get with the usual dream state but I am still self aware and know I am "dreaming". The trick is not "waking" yourself up. I usually like to fly (although I lose control and crash if I go too high... - waking up sharpish) or walk through walls and whatnot.
One example I remember vividly from my childhood was walking around my then family home but despite wanting to could not find anyone; there was nothing to be seen outside the windows save a bright light. I started to feel extremely alone and as a result "woke" up. It still gives me the chills now when I think back on it.