The service panel is the control center for a home's electrical system and must be accessible at all times. It is usually hidden in an out-of-the-way place, but if that place suddenly becomes prime real estate, as when you finish a previously unfinished basement, you need creative ideas to cover the panel. It's either that or move it, and that can be an expensive proposition.
Hang a Picture
The most obvious way to hide a panel is to hang something over it. Many people do just this, taking the opportunity to highlight a favorite piece of artwork or even resorting to a calendar or mirror. A problem arises if you hang a heavy picture over the panel; however, and that is the need to remove the picture every time you have to re-set a breaker. A solution for this problem is to screw a piano hinge onto the back of the frame on the side, and attach this hinge to the wall so that the picture hangs over the panel like a second door. When you need access, you can simply pull the picture and let it swing away from the wall so that you can open the door.
Build a Bookshelf
A bookshelf not only hides the panel while giving you access to it, but it also provides some extra storage space that most houses need. Be sure to space the shelves so that the panel door can open easily, and use large books or other ornaments to camouflage it. You can build a freestanding shelf or one attached to the wall. If you choose to attach it, make it easily removable in case electrical work is needed on the panel. A bookshelf has the extra advantage of hiding exposed wires that are coming out of the panel.
Build a Wall Cabinet
Enclose the panel with a wall cabinet that doubles as storage space. You can build or buy one to suit your needs, and simply cut a hole out of the back for the panel door before you hang it. A variation of this idea is to build a small, shallow cabinet that has no other purpose than to hide the panel, as suggested by Lumberjocks, which consists of not much more than a frame and a door. Make the door from a type of wood that complements the room decor, or simply use fiberboard or plywood and paint it to match the trim.
Hide the Panel in Plain Sight
Go ahead. Paint the outside of the panel. No one says it has to be gray. Create your own whimsical creation with spray paint or paper mache, and use the fact that the door is metal to attach colorful magnets. Make the panel a feature by painting the surrounding wall to highlight it. Sometimes making something obvious is the easiest way to make it disappear.