You don't have to cover small cuts and scrapes. But if your wound is in a spot that rubs against your clothes or may get dirty -- like on your knee or hand -- put on a gauze pad or a sterile bandage.
A bandage keeps the area moist, which helps prevent scabs and scars. The dressing will also keep bacteria out and prevent infection. For deeper cuts, use a "butterfly" bandage to hold the skin closed.