A quick and effective way is to install gnome, remove a bunch of packages related to unity and run lightdm-set-defaults to change your session. I am sure there are other ways and I may have forgotten a few packages, but that's not so important. I have found this to work great for my purposes:
sudo apt-get -y install gnome
sudo apt-get -y remove unity \
unity-2d-places \
unity-2d \
unity-2d-panel \
unity-2d-spread \
unity-asset-pool \
unity-services \
unity-lens-files \
unity-lens-music \
unity-lens-applications \
gir1.2-unity-4.0 \
unity-common \
indicator-sound \
indicator-power \
indicator-appmenu \
libindicator7 \
indicator-application \
evolution-indicator \
indicator-datetime \
indicator-messages \
libnux-2.0-0
sudo apt-get -y install tomboy \
transmission
/usr/lib/lightdm/lightdm-set-defaults -s gnome-classic
We use gnome-classic since it's closest to what you were used to in previous Ubuntu releases such as 10.04 and 8.04. It appears you need to install tomboy and transmission because they might have been removed in the earlier apt-get remove stage.
This works for Ubuntu 12.04 last time I tried, which was a week or two ago. In earlier versions of 12.04 some package names changed, for example libindicator7 was called libindicator6 before. However I believe that since 12.04 is closer to being released the package names should have become stable.
