Laundry Basket
Keep an empty laundry basket in the trunk, and after grocery shopping (or any kind of shopping that involves a lot of plastic bags), put all the bags into the basket. The basket will not only contain the bags on the trip home, it'll make the process of getting the bags inside much easier!
Bungee Cords
Bungee cords can be amazingly useful. Simply stretch a cord across the trunk, attaching it to the hooks, and thread the handles of the bags through it. The bags will stay upright and in place!
Carabiner Clips
These are incredibly strong. Add them to the headrest handles and hang the plastic bags off them. No more tipping!
Simple, inexpensive, and will definitely keep the bags from creating messy, smelly, spills in the trunk!