I can't seem to be able to delete any animations from my list of actions.
How do I delete just the ones I want gone and keep the others?
In the Dope Sheet Panel
In the Actions Editor
Click on the Browse Actions and select the animation you want to delete.
Hold Shift and press the X next to the + sign.
This will add a 0 prefix to the name of the action.
When you reopen the file all marked with 0 will be eliminated from the list.