I agree with Gangta, everyone dreams but not everyone remembers them. And those dreams you do remember are typically the ones you had right before waking up. I had gone years without remembering any dreams and then decided that I wanted to start remembering. The simple mental act of making an effort to remember my dreams began my dream memories upon waking. The additional effort of taking the time to write them in a dream journal each morning actually increased my dream recall drastically. This was about 5 or 6 years ago that I started this. I now remember an average of about 4-5 dreams a night.
And I've gotten to the point that, if I'm having an 'important' dream in the middle of the night, I consciously wake up immediately afterwards so I don't forget it before morning. At first, I would grab my journal and furiously scribble what I remembered in to it at the time (often times around 1-2 am). But after awhile, I got to the point where the sheer act of me waking up in bed afterwards and mentally running through all of the details was enough for me to retain it upon waking. I now will go back to sleep and when I actually wake up in the morning, I'm able to remember the dream and then write it down. All of this has taken practice and effort though.
And I've gotten to the point that, if I'm having an 'important' dream in the middle of the night, I consciously wake up immediately afterwards so I don't forget it before morning. At first, I would grab my journal and furiously scribble what I remembered in to it at the time (often times around 1-2 am). But after awhile, I got to the point where the sheer act of me waking up in bed afterwards and mentally running through all of the details was enough for me to retain it upon waking. I now will go back to sleep and when I actually wake up in the morning, I'm able to remember the dream and then write it down. All of this has taken practice and effort though.