I'm sure some people will call this common sense, but I was surprised when I found out this is possible, and I'm sure there will be other people that are surprised as well.
Shielded/invincible targets are immune to damage, but they are not immune to fears associated with damaging attacks. I would have expected a purely fearing skill like a witchdoctor's horrify to fear them, but the Demon hunter's Elemental Arrow, and Monk's cyclone strike will also fear shielded targets even though they are immune to the damage caused by those skills.
It is also possible that knock backs and chance on hit to fear/knockback on a weapon may work on shielded targets, but I haven't tested any of those to confirm yet.
This is very useful for Demon hunters especially, because elemental arrow passes through targets, so when you run into invincible minions you can fear all of the minions, and damage the main elite all with the same attack.