For tips on recycling old or broken string lights visit How to Recycle Christmas Lights by Recycle Nation or Christmas Light Recycling by Christmas Designers.
Do not put string lights in your curbside recycle bin. If string lights end up going to a recycling center they become tangled up in the machinery causing the facility to shut down in order to manually untangle them.
Most scrap metal facilities will accept string lights. Search for other locations on Earth 911 for recycling string lights.