We've had great luck with the removable 3M velcro picture hangers. (Each corner is held with two pieces of velcro that face each other. The velcro has double back tape on the back, which affixes to the wall and the picture. The double back tape is stretchy, and can be removed by pulling a tab. The tape is single use.

No damage to paint so far, though we've only had them on the walls for about a year.