I want Ubuntu to always use Unity2D by default. I am using the latest version (12.04 LTS).
To set the default for all users, you can use
sudo /usr/lib/lightdm/lightdm-set-defaults -s ubuntu-2d
or you can edit the file
/etc/lightdm/lightdm.conf directly. See this documented version.
Per-user settings are stored in either
$HOME/.dmrc or in
/var/lib/AccountsService/users/$USER . According to this post, the latter file may overwrite your .dmrc.