That title is rather broad, so let me narrow it down. This applies to anyone running XFCE with GNOME services enabled. Maybe there's another, better way to do this, but thus far, I haven't found one.

Even though I've removed gnome-power-manager, my computer still seems bound to the settings in some GNOME power service. Except I can find anywhere to change them in gnome-control-center. Fortunately, I found another way.
Enter 'gsettings'. Think of it as gconf v2.0. Anyway, there's a schema that's the cause of all our problems.

There are two keys in org.gnome.settings-daemon.plugins.power that we need to modify. One is called 'lid-close-ac-action' and the other is called lid-close-battery-action. One guess what they do.
Anyway, here are the following possible values -- or ranges that these keys can be set to.

$ gsettings range org.gnome.settings-daemon.plugins.power lid-close-ac-action
enum
'blank'
'suspend'
'shutdown'
'hibernate'
'interactive'
'nothing'

Those values speak for themselves. The command to change a schema key is demonstrated below.

$ gsettings set org.gnome.settings-daemon.plugins.power lid-close-ac-action nothing

In this case, it sets the lid-close-ac.action to the value 'nothing'. Feel free to change 'nothing' to change any of the other range values.