Using a wall anchor requires you to drill a pilot hole in the wall, tap the wall anchor into the hole with a light hammer and then drive a screw into the anchor. Driving the screw into the anchor stretches the plastic so it can't be reused. However, if you purchase reusable anchors or take certain steps during your project, you might be able to salvage the anchors (see Reference 1). In some areas, old plastic wall anchors can be recycled (see Reference 2).
Reusing Wall Anchors
Once you remove a used wall anchor, the stretching caused by the screw that was in the anchor weakens the plastic. This makes it difficult to tap the anchor into a new pilot hole without the anchor collapsing under the pressure of the hammer. However, if you haven't driven a screw very deeply into the anchor, you can pull out the screw and reuse the anchor by reinserting just the tip of a screw into it. Use a pair of pliers to grip the screw and pull straight back. The wall anchor will be dusty, but still usable.
Reusing Anchors and Screws
If you've already driven the screw into the wall anchor, you may still be able to reuse the combination anchor and screw. Loosen the screw so half of it is in the anchor and the other half is exposed. Take your pliers and pull straight back to remove both the screw and anchor at the same time. Because the screw is still in the anchor, it provides some support for the plastic as you tap it into a new pilot hole. The new pilot hole may need to be slightly larger than the original one to accommodate the screw and anchor.
Buying Reusable Anchors
Take the time at the hardware store to look for reusable wall anchors. The package clearly states that the wall anchors are reusable. Reusable anchors are made of sturdier plastic than traditional wall anchors and costs a little more. Pay attention for packages that say the anchors are "removable." These anchors can be removed easily, but are not necessarily reusable. (see Reference 1)
Recycling Wall Anchors
Because wall anchors are small and made of plastic, they can be difficult to recycle. Even if your waste company accepts plastic, they may not want pieces that are smaller than a yogurt container. However, your waste management company or local environmental group can help you find a recycling center that accepts plastic wall anchors and other rigid plastic items. (see Reference 2)