Who Dares Wins said:
Nothing would happen. I don't dream. And it's not "last night" it's the last 1 minute or so, of your sleep. Please correct me if I'm wrong.
Everyone dreams, it's just if you remember them or not. And the deeper you are into your sleep cycle, the more they occur. You also have loads a night and the closer you are to waking up, the longer they last.
If you want to dream more, try falling asleep as soon as you wake up (Or set your alarm for 1 hour before you normally get up) you are almost guaranteed to have a dream that you will remember.
As you have loads of dreams a night, you forget about the older dreams which you had earlier in the night and you are more likely to remember your dream just before you wake up. Some people, like yourself, don't seem to remember any dreams. However, I can remember dreams back from my childhood :S
PM me if you want to know any more.
Ironically, I can't remember my dream from this morning *Fail*