Paint the hinges to match the door and trim around it. Use a metal spray paint on the hinges before installing them. It is easiest to hide the hinges with paint if the door and trim are the same color, such as a white door and white trim.
Install the door hinges on the inside of a cupboard or cabinet. This hides the hinges when the door is closed. When the door is open, the hinges will only be slightly visible. Barrel hinges are small and don't take a lot of room so they won't be visible. Choose hinges that match the cabinet color or paint them to match to make them even less visible.
Obscure the hinges from view using portable objects. This works best on a door that isn't frequently used. Try hanging entry curtains, such as Japanese door curtains, or beaded curtains. Place tall plants on each side of the door to obscure the hinges. Use either silk plants or real ones. Hang a long, narrow flag or banner from the ceiling so it drapes down in front of the hinges.