I got my Dad the Ottorbox Defender case - he's in his late 60's with a long history of pagers/cell phones ending up in snowbanks, toilets, falling out of his pocket from a ladders, etc. He LOVES the case. He got impatient and got the phone before the case arrived, and he commented several times that the phone was too slippery for his "old man hands" without the case. I went up over Labor Day and saw the case for myself, and it's a really great case that will provide a lot of protection. Even though it's a substantial case, it feels really great in your hand and doesn't get in the way of using the phone at all.
I'm coming from a TBolt that I had to carry caseless b/c every case I tried made the buttons too difficult to access, but I didn't mind because I've had a cell phone since '04, and I've only ever had two real drops. One cracked the camera on my old school Razr, the other was my EnV2 down an elevator shaft (for the record, 3 stories, worked fine once I got the maintenance guy to recover it. Still have it, and recently gave it to my mom to replace her super old phone). Maybe I'm lucky, but I don't drop phones (I do crack MBP displays though, so we all have our thing).
For my S3 I only got a case b/c I have the white and was worried about the back getting scratched up on it. I have the Speck Candyshell case (white with pink accents). I LOVE it. It does make the phone easier to hold and gives it some heft (there's such a thing as too light IMO), and makes the buttons easier to push. It's also very attractive - even the guys at work were like "Whoa" when they first saw it. It does add some bulk to the phone, but you don't feel it at all.
I have a screen protector but I just haven't taken the time to put it on. I put one on the first S3 I had (swapped my 16 for a 32) and it was not a fun process, nor was I overly thrilled with it, so I'm still doing some research on that.