I use a pair of REI shopping panniers for grocery getting, office supplies, and laundry. I don't like the hooks that just hang over the top of the rack but the spring and hook at the bottom seems to hold well. Once I nearly kicked a pannier off with my heel but fortunately only one hook at the top popped off the rack. But all in all it was a very well spent $40 with shipping. I use them at least 4-5 times a week for assorted errands and definitely for hauling home groceries. I also hang them in the grocery cart to make sure I don't carry too much home. I have a handlebar basket that carries bread or eggs or delicate fruit -- very handy.
In the future I want to buy a trailer to bring home bigger items like large bags of flour, gardening supplies, and bulky stuff like toilet paper.