As far as I'm aware, you do threaten your square:
Most creatures of Medium or smaller size have a reach of only 5 feet. This means that they can make melee attacks only against creatures up to 5 feet (1 square) away.
If a Tiny creature is in your square, I'm used to being able to AoO that, as well.
For movement, it specifies that it's threatening opponents that can take AoOs:
Moving out of a threatened square usually provokes attacks of opportunity from threatening opponents.
But most things simply say that an action provokes attacks of opportunity, and doesn't clarify who is allowed to take them.
It may seem silly to ask if you can AoO yourself, but in certain builds it can actually be useful. Is there any RAW clarification on whether you're allowed to take AoOs against yourself when you provoke?