CloudApp can do this for screenshots or any file in the finder, plus copies a link to the clipboard: http://www.getcloudapp.com/ (not affiliated, just a very happy user)

Can't all screenshot tools do this, just by you telling it to save them into ~/Dropbox ?

What chrisbolt said, but this also notifies you via growls, allows you to control whether each screenshot is posted and allows you to specify a filename. :-) And, of course, copies the link to the clipboard.

I haven't found another one that automatically puts a URL to the file at Dropbox on my clipboard.

defaults write com.apple.screencapture location /Users/.../Dropbox

does exactly that on Mac OS.