Google Font Directory
Here’s a script that can be used to download and install all the Google Web Fonts. 

What the script does is download all the fonts from Google Font Directory (it includes around hundreds of fonts, each with many variations that you can use on your desktop or various designs), and installs all the ttf fonts under /usr/share/fonts/true-type/google-fonts (so if you want to remove them, simply delete that folder).
To download and install all the Google Web Fonts in Ubuntu, open a terminal and type the following commands:
cd && wget https://raw.githubusercontent.com/hotice/webupd8/master/install-google-fonts
chmod +x install-google-fonts
./install-google-fonts

If you want to take a look at the script before running it, download it from HERE.

Once the script finishes downloading and installing the Google fonts, you can go ahead and try them out. If you want to use one of the Google Web Fonts for your desktop, right click your Desktop, select “Preferences” and set the new font on the “Fonts” tab.
The script creates a “fonts-master” folder in the directory where you run it (your home folder if you’ve followed our exact instructions). I decided not to delete it from the script since you may need it.

Update: the script was initially downloading the Google fonts via Git (initially via Mercurial) however, since there are now so many fonts, the “git clone…” command used to time out quite often, so I decided to update it to download the repository master as a single .tar.gz archive.