Dropbox's latest build (still an experimental one) allows you to capture your screenshots and shares it with your Dropbox account. This feature is currently supported in Windows and Mac only.
For Windows users:
While Dropbox is running in the background, you need to press Print Screen on your system and a screenshot of your screen is copied to the Dropbox folder as well. Another awesome feature is that if you press Ctrl+Print Screen, then a link of this screenshot is copied to your clipboard as well and hence you can share it instantly although the file is still being uploaded. (All screenshots are public).
For Mac users:
Use Command key + Shift-3 and you can also press the Control key to copy the link to clipboard/
If you wish to disable this feature, go to the Import tab and deselect the Share Screenshots option.
You need to install the experimental build first in order to do so. You can download it from here
and there are a few other additions as well about which you can read in the link provided.