I flatter myself that I've perfected the process of brainstorming, and it's not just boasting to the extent that I can't recall the last time I didn't have an operable project, or one within an hour of realizing I had exhausted by previous list. Last time I described my process to a friend they described it as being very systematic and I don't think that's wrong. For the most part I don't bother with intentional prompts, though I've never turned down a prompt if it sparks something, obviously.
I have three major methods: audio method, puzzle method, and music method. I alternate between them as much as possible so none of the three become stale.
Audio consists of me finding an old radio show, or segment of found audio from my archive (I'm a rabid audio archivist. I download and record all kinds of weird audio files.) and, putting myself into a receptive state, just listen and wait for clips and phrases that I feel like writing down. When I'm done, I've usually already shaped out a story from them, and from there it's just working out details. The sweet spot is about one hour of audio.
Puzzle method has me sitting and doing a crossword, usually though I've used logic puzzles and others in the past. This is a little more direct, but what I'm writing down here are favorite words and juxtapositions of words from the puzzles. Non-themed, non-cryptic crosswords work best for this because the clues and answers are more arbitrary.
Music is the most straightforward of all. While I've conceived of doing stories built from specific albums, generally I use a randomly generated or found playlist. Stumbleupon used to be great for this, and I miss it very much. This method sees me building a story a scene at a time, based on order of songs. This is my most thoroughly methodical style of brainstorming, and requires either simultaneous outlining or straight up writing as I go to be effective.
Most of all, I think it's just a matter of training your brain to see the story potential in anything, and to open yourself up to so many kinds of stories that you don't miss one just because it isn't what you're already doing. So finally, and this isn't a method, I just pay attention to everything. More than just sometimes a story just pops out of the chaos of every day existence.