Officially recycling grocery store type bags is a community waste hauler policy issue. Most don't want them in the curbside single stream recycle bin picked up. They are considered soft recyclables and not hard recyclables like milk cartons, water bottles, and etc. So, best take caution and check the online websites for the waste hauler. Below is the quote for my local carrier Escondido Disposal:
Soiled disposable plates or cups, soiled paper towels, soiled tissue, carbon paper, plastic bags (NO plastic grocery bags, newspaper delivery bags or chip/snack bags), ceramics, drinking glasses, Styrofoam packing peanuts, mirrors, batteries, light bulbs, clothing or shoes."
Some grocery stores such as Walmart have a recycle drop off point for them. At some of the Albertson's stores local to me there are bins at the entry to drop them off at. Not sure of other chains. So, it is convenient to drop them off when I go shopping.
Otherwise I use them for my bathroom trash bins, which are small. I use them for carrying stuff like tools when I go away from home to a friends. I use them for filler when I ship an Ebay item I sold. I used them to beef up a pillow once putting the side with bags downward. I use them for long time storage for closets. Most are white so easy to use a magic marker.