Take inspiration from what professional art galleries use - they often have a slot in the wall that little hooks slide into. These hooks are connected with thin wire with hooks at the end for hanging the art work.
But you don't want to make a slot in your wall - too messy and too much work. What I had planned on doing at one time was to fasten a small piece of wood, say 1"x2" to the wall. Hammer small nails into the top at regular intervals. Paint all of this (wood and nails) the wall colour, so it blends in. Buy some fishing line and make a loop at the top to go over the nail and then tie a hook at the other end.
This solution is almost invisible, is not limited to light weight art pieces, and (very important!) is cheap and easy! As a bonus, it will only leave a couple of small holes in the wall if you screw the 1x2 strapping into the studs.