The safest 2013 SUVs w/ 5-Star Safety Rating. The list of 2013 safest SUVs are highly recommended SUVs if your main concern is safety. Car safety is on of the most important things to be considered while buying a new vehicle. SUV safety features are incredibly important with the extra risk from driving that type of car. This list includes both small and mid-sized SUVs and all the safest SUVs available on the market.