Endoself mentioned lucid dreaming; in the few lucid dreams I have had, I knew I was dreaming, but in the many normal dreams I did not know. In fact, non-lucid dreams feel extremely real, because I try to change what's happening the way I would in a lucid dream, and nothing changes - convincing me that it's real.

When I am awake I am very aware that I am awake and not dreaming; strangely that feeling is absent during dreams but somehow doesn't alert me that I'm dreaming.