Mostly I write because I get the 'strange' feeling. Something will hit me as being meaningful or metaphorical in a way I hadn't thought of, and I'll try and put words to that feeling.
I can definitely relate to that - you've pretty much captured my experience of 'inspiration', when an unforeseen possibility calls out for expression, and seems to be within reach.
I use many different methods, often making up the rules as I go along - sometimes I go for fluidity of form, whereas other times I'll impose strict formal constraints (e.g. line lengths, stanza lengths) and try to work within and around them.
If I'm not feeling particularly inspired I'll either go back to work on older stuff, or play around with cut-ups and try to get a spark from there. I collect strange and interesting words/phrases in my notebook, and I'll often pluck phrases from here and there and start assembling them, morphing, cutting, rearranging, juxtaposing, etc.
I often think of my writing and editing methods in terms of electronic music production, part sampling and part sound-generation/manipulation. It's just an analogy, but one that works for me. I also like to experiment with 'textual remixing' (remixing someone else's work, with their permission - or giving someone a piece of mine to remix).
Raz, I know what you mean about 'editing the soul out' of something. That's a genuine risk, but on the other hand I don't necessarily subscribe to the 'first thought, best thought' philosophy either. That's generally attributed to the Beats (Ginsberg, Kerouac, et al), but in fact those guys were compulsive revisers/rewriters. The myth says that Kerouac wrote 'On the Road' in 3 weeks on a continuous roll of paper, but that was just the first draft. Plus he'd done plenty of note-taking and planning beforehand.
To quote Sol Stein: 'The biggest difference between a writer and a would-be writer is their attitude toward rewriting ... Unwillingness to revise usually signals an amateur ... [W]riting is truly rewriting.'
Although like you say, we're not all aiming to be 'professional writers' (whatever we take that to mean). Speaking for myself, I make a portion of my income from writing, and another portion from teaching writing and editing. So in one sense I'm a professional writer. But when it comes to my passion (poetry and experimental writing) I wouldn't use the term 'professional' in that context. I'd say that I'm dedicated to my chosen artform.