Of course, you can wear sunglasses when you are running. As we know that nowadays, there are many people who like fashion will wear sunglasses when they have activities. By wearing them, it can make them look cool and have attractive image to others. But on the other hand, you should know that sunglasses can also be beneficial to your eyes too. For example, there are many sunglasses which are designed to protect your eyes from the UV rays and the strong sunshine, for they are UV protected. So when you wear them outside to have running, you do not need to worry about the damage coming from light. Anyway, you can wear them.