Unity is the default desktop session in Ubuntu12.04. Gnome is not included in the package.
There are some article taught how to install Gnome Fallback to activate Gnome. The command is
sudo apt-get install gnome-session-fallback.
After it is installed, you can pick up Gnome Classic in the login list.
It really does work in Ubuntu 12.04.1 alternative package.
But I got error while run the command in ubuntu 12.04.1 Desktop version.
After the investigation, it is caused by the different source server. Once change the server location to correct one. Gnome fallback can be installed correctly.
In ''Update Manager"-->"Settings"-->"Ubuntu Software" tab-->"Downloaded from" change to ''Server for United States".
And then run 'apt-get update' to update the repository. After it, run 'apt-get install gnome-session-fallback'. Enjoy!