Dropbox definitely makes sharing files super-easy, with the right-click Copy Dropbox Link in the file system (if you have their sync client installed, and you should). However the link they give you opens a web page that has all sorts of Dropbox chrome cluttering things up. What if you just want to share the raw image?
It's actually a pretty simple tweak. The link they give you looks something like this:
Notice the part at the very end that says dl=0. That actually means "do no download the file; show it in the web browser". [Protip: computers use 1 to mean yes or true, and 0 to mean no or false.] Actually, you don't even need this part of the link for it to work, so I'm not exactly sure why Dropbox includes it.
If you delete that part of the link and replace it with raw=1 ("Yes, show the raw image file"), then the link will show just the image. So now your link looks like this:
A word of warning: Dropbox leaks your account display name when you share a file. If you open the first one above, you can see in the right column it says <username> will be notified. If you care about this, be sure to change your display name to something generic like I did.