If you want to turn off the Recent Documents feature in Ubuntu, all you have to do is create a .gtkrc file in your home directory (if one isn’t already available):
Now paste this line in there:
The next time you start Gnome and click on files, the respective files won’t appear anymore in Places > Recent Documents.
To limit the number of files that appear in Recent Documents, use
instead (replace 3 with the number of files you wish to show).