I've done various kinds of writing both professionally and for my own satisfaction.
If it's professionally, I'm inspired to write by the fact that I have to, basically.
actually, it has always helped me when others set deadlines for me. But I don't think that's really what you're getting at.
I used to write fiction but haven't for several years. Basically, I think I am a good writer stylistically but I tend to have a lack of creative ideas plot-wise...it is just not my thing...I have often talked with friends about this, since many of them say they have plotlines coming out of their ears but can't write to save their soul. I think we should get together and collaborate.
These days my main form of creative expression is poetry and I think it is really my voice. It seems to me to get closer to the truth of the way things are than any other form of writing, and maybe even any form of art...yeah, I'm that obsessed.
I read a lot of poetry (mostly modern, like WB Yeats and after) and that gets the juices flowing. I find I am often inspired to write poems about places I have visited, though it's usually after the visit, not while I am there. Also, whether the ostensible subject of the poem is a city I have visited, or anything else, it usually unfolds my subconscious to me in a very interesting way...I mean, I will be writing, and I think I know what the subject is, but by the time the poem is complete, I realise that more than the place I'd visited (or whatever) the poem is about whatever is on my mind - whatever it may be - questions of relationships, ethics, specific people I'm obsessing about whose shadow creeps into the poem, etc...
One of my resolutions is to force myself to write more, though. It's like anything, you can't just rely on inspiration. I think I need to set myself some exercises and just write - even if a lot of it is not much good, at least I will be writing and revising and developing and practising...