Curtains should hang either below the windowsill or above the floor. Try to have it no more than 2 inches below the windowsill or 2 inches above the floor. While these numbers are standard recommendations, having your curtains an inch higher or lower will not be that much different.
If you have small children or pets, low curtains can be a potential hazard. Children and pets can pull on them and have pieces of the curtains or even the curtain rod fall on them. Low-hanging curtains can also turn into chew toys and cause choking.
While curtains hanging right below the windowsill or right above the floor are traditional designs, keep in mind of low-hanging curtains and their potential hazards. Always opt to hang curtains higher if you think it is necessary for safety reasons.