I'm currently a level 56 Demon Hunter with a crossbow and quiver. The best quivers I've seen give significant damage boosts, although with my bow it's not necessary (able to kill normal mobs relatively quickly on Hell difficulty). I've read that using a shield as your off-hand, typically something high in dexterity/vitality, is beneficial since Demon Hunters aren't the strongest class. While solo-ing I get low on health frequently (although I regain it pretty quickly due to near-constant crits and lifesteal), but in group play I'm almost always out of the line of fire.
Long story short, why (and when) should a demon hunter use a shield?
Best Answer
Well, I think the main issue is that a shield on your off-hand restricts the weapon you use on your main hand to a hand crossbow, as opposed a quiver on your off-hand which lets you use two handed bows as your main weapon.
But other than that, i can think of no reason why using a shield would be inherently bad, other than the fact that you need a good hand-crossbow to go with it. In fact, a shield with a good dexterity stat can increase your DPS as much as a quiver, while also increasing your defense and survivability much more than a quiver could.
I think it comes down to what specific items you have and what balance of DPS and survivability you want. Turn on advanced tooltips, and play around with equipping different weapon combos, and see how your damage/armor rating changes. Sometimes using a shield will be better, and sometimes it won't.