For very limited protection I use this case: Samsung Protective Cover for Samsung Galaxy S6 Edge - Clear Silver

By far the slimmest case I've ever used on any phone.. It mainly protects the back and corners, the top and sides are completely open. It's my day to day "case".

The more rugged case I use: Incipio Dualpro Shine

Another great fitting case. This one has more protection all around, including the top/sides. Still feels awesome in your hand, slim and sturdy.