Paint the closet door using the same color of paint that was used on the walls. Doing so continues the flow from the wall to the closet door and allows the eye to skip over the door.
Replace large or clunky doorknobs with discreet furniture pulls. Choose pulls that can be painted to match the wall and the closet door itself. Doing so calls less attention to the closet door.
Place a bookcase or another large piece of furniture in front of the closet door. This blocks the door entirely, and it also focuses the attention on the furniture rather than the door. A bookshelf or even a bed are two options.
Hang a tapestry over the closet door's tacks. A tapestry will cover the door entirely, hiding it from view, and the tapestry will also add color and texture to your room. You may also use a quilt or another large piece of material for this purpose.
Hang a picture up on the closet door. A picture shows people that the closet door is typically and commonly kept closed, and it also distracts the eye.