I noticed something in OD&D I overlooked before: the undead might have to make morale rolls.
This came up because of the recent Delving Deeper errata. There's a note that ghouls have -2 to morale rolls in daylight. That's not in the LBBs, but it turns out that it *is* in Chainmail. In fact, Chainmail lists morale numbers for wraiths, specters and vampires, too. Only skeletons and zombies are fearless.
In contrast, the AD&D monster manual says that ghouls attack without fear. I seem to recall that later AD&D materials explicitly exempt undead from feeling fear -- so, no morale rolls.
My first reaction was "Screw it, the living dead shouldn't be afraid of anything except a cleric showing true faith. The Turn Undead roll is the only morale roll needed."
But we do have vampires afraid of the cross and of garlic. And a fear of sunlight or bright light isn't too far from genre expectations. Also, holy water. Not to mention that we could add unique fears to unique undead: forcing a ghost to view its own corpse might act like Turn Undead on that corpse, and zombies might be afraid of carrion birds.
So my current thinking is: the undead are not afraid of simple death and cannot normally be intimidated, but certain symbols of faith, light, or purity can trigger morale rolls.