With the release of version 10.10 comes a new set of fonts, named Ubuntu. If you're not ready to upgrade to the new version just yet, you can install just the new fonts by downloading them here.
Just double-click the downloaded file to run the installer. You'll have to change the fonts used under System -> Preferences -> Appearance -> Font; change The Application, Document and Desktop fonts to "Ubuntu", the Window title font to "Ubuntu Bold".
If you're using Google Chrome, you can install this extension to use the new fonts. You will probably have to change the default fonts under the preferences menu.