Many of my stories came along as simple random thoughts, usually in the middle of talking to someone about mundane matters. Most recently I was talking to one of my writing friends about a short story challenge. She had dreamed up a good story idea, only to have it fade when she woke to the cat's nudging. Thus I proposed a theory about cats and dreams that is now on my list of pending stories.
That list of pending stories has grown sizable already, and will likely never be completely written. This is not a real problem; the real problem comes in restraining myself from diving into this list while I still have a half-dozen projects in active working status.
Working on multiple different projects at once has benefits as well as drawbacks. One benefit is that my mind can ponder possibilities of a story line while I'm working on something else completely. I don't get burned out on one particular story because I take a break from it to do something else. One of the drawbacks is the possible blurring of characters.