Now 3 yrs have passed, and seems more modern browsers (Chrome, FF; not sure about IE) support pasting image through clipboard using javascript and php/jQuery.
http://strd6.com/2011/09/html5-javascript-pasting-image-data-in-chrome/
There are some hints on stackoverflow too:
http://stackoverflow.com/questions/361324/pasting-an-image-from-clipboard-to-a-website
http://stackoverflow.com/questions/6333814/how-does-the-paste-image-from-clipboard-functionality-work-in-gmail-and-google-c
And here is one more example:
http://joelb.me/blog/2011/code-snippet-accessing-clipboard-images-with-javascript/
I wonder if it possible to integrate it with media manager?
It would make much easier to get screenshot(s) added to dokuwiki document, just now its too many steps to save and upload - like jamsden already described.