If you're using GNOME 3.x then you can adjust clock setting using gnome-tweak-tool. However, you can take out the the date but not the day (i.e. Sat cannot be changed so far as I can tell)!
sudo apt-get install gnome-tweak-tool
You can also look in g-settings via a terminal:
gsettings list-keys org.gnome.shell.clock
gsettings set org.gnome.shell.clock show-date false
gsettings set org.gnome.shell.clock show-date true
which gives only two options: show-date or show-seconds!
Or you can open up the configuration editor, then open "org" - "shell" and you will see calendar and clock which you can change manually.
When you open the Tweak Tool and go to Top Bar, you will see the option for showing/hiding the date:
Best Answer
Not sure when this path changed, but as of Ubuntu 13.04 the seconds display can be set in the terminal with:
To turn seconds display off:
and checked with: