When you sleep, the brain releases a myriad of inhibitory neurotransmitters. Some are to stop you acting out your imagination, like sleepwalking, others are to stop you remembering what happens in your sleep, since dreams largely contain nonsense information. Some people just have more effective inhibitory mechanisms than others.

I never remember my dreams if I get a good nights sleep. However if I am suddenly woken by a phone call or if I am really tired, I may remember tiny pieces of a dream since these things can interrupt the inhibitory processes and thereby allow the information to flow into my memory.

I find that if I awaken naturally, I don’t remember dreams. If I’m awakened in the middle of a dream, I’ll remember it.

Because the first few seconds after you wake up consciously or subconsciously you have to remember who you are and where you are and whats going on.

Some people don’t remember their dreams because the do not have good dream recall, we all have the ability to remember all of our dreams but you need to train your mind to do so.

As @FireMadeFlesh said, your memory is stopped while you are asleep. Or rather, your long term memory is not at work. Short term memory is still there. That is why we remember things for a moment and then they are gone.

In order to remember dreams for a longer time, you have to make an effort. As soon as you wake up, you have to go over the dream in your mind, as much as you can. Replaying it. This allows you to transfer short term memories into long term ones.

A lot of people keep dream journals for this purpose. You quick write down the memory as soon as you wake. This has the added benefit that if your long term memory is still too sleepy, you have the written record to remind you.

If a dream is shocking enough, it may transfer over to long term memory whether you try to make it happen or not. My guess is that this kind of shock somehow wakes you a bit, allowing things to move into long term memory.

Firemadeflesh is correct, although I would explain it as your “information filter.” Everyone’s brain has a filter that allows you to remember stuff that is important and discards stuff that is not important. Your dreams automatically go into the “discard” pile. If you are suddenly awakened, you might be able to “snag” that memory before it vanishes. Case in point is Kim Peek, the real Rain Man. He was a perfect example of a person who, due to brain injury, did not have an information filter. He could instantly recall any fact that he had ever heard or read. Very interesting stuff. We really know so little about how the brain works.