I have a pair of REI panniers ($40), which I haven't used yet for groceries. I used to have some Nashbar panniers ($30 or so) which I did carry groceries in. I packed just like you would a grocery bag, heavy stuff on the bottom, light and fragile on top. The drawstring top molded itself nicely to the contents, and the buckled flap kept things dry and secure. I didn't cart groceries in heavy rain, though. Eggs didn't break, but I took it slowly.
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson