I have a Samsung Note 2 and use only a screen protector (high quality one with silicon adhesive, Steinheil I think).
I had a phone cover for my Note 1 and it really did make it too thick, as most of them do. It also didn't seem to help when I dropped it on the stairs at home and it landed almost face flat. The display inside the device broke, but interestingly enough the glass touch panel didn't.
I've dropped my Note 2 quite a number of times (a couple of times onto concrete and asphalt) and the only damage so far are some scraped edges, a slightly flattened corner and what looks like some kind of point impact crack on the back panel (it's plastic, but has some kind of coating on). Everything still works like they day I bought it
![Smiley :)](https://cdn.geekhack.org/Smileys/solosmileys/smiley.gif)
Newer Samsung model phones are really tough and seem to be able to handle
almost as much abuse as those older Nokia Symbian phones (although those are simply legendary in terms of what they can handle), so I don't consider a cover necessary for them. Can't really say about other brands / models.
@tp4tissue: How do you live with that OS on your device? It doesn't support USB OTG so you can't use an external keyboard with it
![tongue :p](https://cdn.geekhack.org/Smileys/solosmileys/tongue.gif)