You can boot into a text screen, if you change a boot option, and from the text screen you can easily start an X-window graphical desktop environment. But you cannot run graphical applications without a graphical desktop environment. If you have several screens, they can be run in different modes.
An alternative is to run the primitive openbox session without a desktop environment such as LXDE or XFCE.
Change a line in /etc/default/grub to
and make it active by the command
GRUB_CMDLINE_LINUX_DEFAULT="quiet splash text"
I use the following script to start X in Ubuntu 12.04
I store it in the file ~/bin/x and I have added the following line to the end of .bashrc as a reminder.
ans="$(ps -A|grep \ lightdm$)"
if [ "$res" == "0" ]
echo "x (lightdm) is already running"
echo "x will be started:"
echo "sudo service lightdm start"
sudo service lightdm start
echo "x to start the graphic desktop environment lightdm"