There are quite a few programs that can do that. One of the most well-known is Tomboy, and Screenlets is another option.
Part of the default Ubuntu installation
Tomboy works great with Dropbox!
Other program is through Screenlets:
- In terminal type
sudo apt-add-repository ppa:screenlets-dev/ppa
sudo apt-get update
sudo apt-get install screenlets
Go to Application > Accessories > Screenlets
In the Screenlets-manager window select the screenlet "Lipik"
(click on it)
If you want notes to automatically start on log-in check the checkbox "Auto start on login" (bottom-left side)
click "launch/add" (left side)
if you do not want notes to stay always above other windows,
right-click on the top of note > Window > uncheck "Keep above"