I keep mine in a "Poetic Palette Ultra slim Hardshell Case for Nokia Lumia 1520 Sand Black" (do a search for that on eBay), that cost me less than $8.
Why?
I started out not liking cases for phones, but the 1520 is just so "slick" feeling I really did worry about it dropping onto a hard floor and breaking. It's larger than any other phone I have used (obviously), so needed to feel better about holding it in my hand. This case has a nice embossed surface that I can grip without the phone feeling too slippery.
Before I inserted it into the case, it wasn't scratched or anything and I think that after ten weeks of use, it will hold up really well.