I havelooked into many cases and put a good number of them onto my phone looking for ones to buy. Most of them that are extremely thin do not cover up and around the front of the bezzle, they are more protecting from the back and around the sides and most don't cover the top and bottom because of the microphones that are there.
There are the silicon cases that protect all the way the phone and bezel, but they are a bit thicker than the thin plastic ones, but not much.
Go to just about any mall and you can try on 5 or 10 and see if you like varying styles.
Google TPU cases and you will find a host of colors in very nice, very protective cases. Amazon.com has them for around $6-$10 each. The TPU cases are one piece, flexible, semi-transparent and cover the back, top, sides and wrap around the edge of the front. Excellent cases.