No Idea on a percentage but i would think very very few people would bother using quotation marks, other than those of us checking SE positioning ;-)
Don't know the %. Do you have Google Analytics (or other traffic analytic software) installed in the site? If so you can tell what keywords are generating traffic to the site. If you are ranking for THE KEYWORD and "THE KEYWORD" you will be able to monitor the %'s and answer your own question. On a different note: I think that traffic sent by searchers using ""'s are more targeted and should convert better.
I rank #3 for the heavily searched term funny pictures. I see atleast 100-200 hits a day from just the keyword "funny pictures" in quotes. So I'd say people do it, but no where near as often as the normal phrase without quotes. Plus if your SERP for that keyword is in top 10, you usually rank top 10 quoted anyways. Hope this helps.