TPU (that firm rubbery material), polycarbonate, and "vegan leather" (aka polyurethane fake leather) are probably the most common materials. If you want to pay a lot, you could find genuine leather cases, mostly from higher end stores like Coach. I think TPU can absorb shocks a little better, given its rubbery consistency. Be cautious with metal cases, because some metals might interfere with cell or wi-fi signal.
I would also caution against cases with a clear plastic back if you do any wireless charging. I got a
Rearth Ringke Fusion case for my Nexus 5, and noticed that the clear plastic back tends to heat up significantly when on a wireless charger, while it never gets that hot with TPU cases. My guess is that the clear plastic doesn't dissipate heat as quickly as TPU.
