I often use my 42 litre panniers for shopping as they are a single pocket design and do just what AGG does... clip them to the cart and fill them so I know my limit.
I have a good number of re-useable grocery bags that I use for larger shopping trips and the most convenient method for this is to take my trailer which can carry enough groceries for weeks.
Living centrally helps and I am very close to many nice stores so a few small trips a week is not a big deal.