So, when is a foe "unarmed"? A quick search didn't net me anything useful.
The first place I looked was Improved Unarmed Strike, which provided this gem of insight: "You are considered to be armed even when unarmed—you do not provoke attacks of opportunity when you attack foes while unarmed...Without this feat, you are considered unarmed when attacking with an unarmed strike".
This can be interpreted in (at least two ways):
A) You qualify for both "unarmed" and "armed" status, and your unarmed strikes carry the exception "does not provoke opportunity attacks".
B) Even though you count as unarmed by a common-language understanding of the term, you do in fact count as armed for rules purposes. As a clarification of what that means, your [unarmed strikes] do not provoke attacks of opportunity.
Interpretation A is silly, and inconsistent with the known writing style of the developers.
So, enemies who have Improved Unarmed Strike are never disarmed.
Gauntlets: "This metal glove lets you deal lethal damage rather than nonlethal damage with unarmed strikes. A strike with a gauntlet is otherwise considered an unarmed attack." An attack with a gauntlet is an unarmed strike, so a foe with nothing but gauntlets is obviously unarmed.
Natural attacks, aka natural weapons, can't be disarmed. But maybe you can use some of those trickster abilities to make them grab a non-weapon in their claws and be unarmed that way.
Armor spikes? Armed.
Shields? ....Well. I want the answer to be "unarmed", but I can't really argue for it.
Some kind of object that isn't really a weapon: IMO, it doesn't count as a weapon until it's been used as a weapon.