Can we connect a normal earphone / headphone to a Android device?

Can we connect a normal earphone / headphone (those that we connect to the Desktop PC) to the Android phone or devices? This is because I notice that the one on the left (the original one that come with the phone) have 4 connector but the one we use on Desktop PC have 3 connector. Was wondering if it will short-circuit and damage the phone or the port itself.