As a lover of prose myself, I believe that writers are slightly crazy. In order to create believable characters in one's work, one has to personally believe in said characters. Seeing in the mind's eye people who are not alive, places that are not real, and events that never happened.
There's a monster in the new Doctor Who series called the Weeping Angel that is truly terrifying in that it only moves when you're not looking, and even a projected image of it causes it to become real. This concept can be seen as the embodiment of any imaginary character: once you imagine, write, or draw it, it becomes real for you.
Ideas pop up in my head frequently. Sometimes I'm inspired enough to write them down, sometimes I'm not. I've had characters that I wrote about 20 years ago reappear, as if to say "my adventures aren't over, write some more about me!" Much of the time I don't, because the scenario is too complex or too outlandish to be believable anywhere other in my own imagination.
Somewhere in the mess that is my home office there's an old notebook in which I scribbled down some of these ideas, and upon re-reading it months or years later I shake my head and say to myself, "it seemed like a good idea at the time, but even I can't believe that." Perhaps it's just as well, because once I start believing in my own imagination, people will think I'm crazy.