We're having a BBQ tomorrow, so I headed to the grocery store today for supplies:
In the left pannier: a good sized watermelon, a half gallon of ice cream, plastic cups, bowls and plates, mint tea bags, and kitchen sponges.
In the right pannier: a pound of cherries, a couple of nectarines, regular tea bags, and three bags of chips (they were on sale). Cokes down the middle on top of the rack.
I went to the store (also by bike) yesterday for other stuff, and will probably go again tomorrow for ice and hotdog buns. I suppose that if I had an enormous freezer and a big car, I could do one giant shopping trip, but given that I always seem to forget something I need, it's not a huge hardship to me to do it in medium size chunks, which are perfectly manageable by bike.