There are many ways to reuse the plastic bags that cover your daily newspaper:
Keep in your diaper bag for dirty diaper disposal.
Keep in your bathroom to place used sanitary napkins inside. Drop it in, tie it up and toss in the trash.
Keep near your kitchen sink to put food scraps in while preparing dinner. If you compost you can dump the food (but not the bag) in your compost heap. If you don’t compost, tie up the bag and toss in the trash.
Tie a couple onto your dog’s leash. They’re perfect pooper scoopers.
Keep in the car to use as trash bags. Fold the top over so the bag keeps its shape and place inside your door pocket.