I've got the S4 - because I carry the phone around in various pockets, I really need a case & screen protector...
I started with a Spigen Armour flip case, but when I folded the case back to use the phone, the magnet kept putting the phone into sleep mode. So I exchanged that for the Spigen Neo-Hybrid Armour case. Nice protectection from small drops, and the raised edge keeps the screen off what ever surface I'm stupid enough to put the phone on face-down.
I'm a huge fan of the massive screen, with it's superior quality... but not too much of the highly refelective surface - so I've fitted an anti-glare screen protector to it. The quality of images etc on-screen doesn't suffer too much, perfectly acceptable. Still gets marked up in my pocket, though...
(maybe I should stop carrying so much other cr@p in my pockets...?)
In saying all that - I'm getting rid of the Spigen Neo-Hybrid case and going for the S-View - all around protection plus the sleep-mode window.
Sooner or later, I will find something that I'm happy with.
Although.... I'm looking at a full armour case for when I'm on the bike (especially on track days), just in case...