I bought 2 of the Nashbar grocery panniers about 2 years ago and have carried gallon jugs of cooking oil as well as massive quanitities of tinned soup when the store has a sale. A lot of weight, in other words. The panniers seem quite sturdy and I'm happy with them in general, though it would be nicer if they had integral strap-over tops. They do come with "shower cap" tops (hidden in a zippered compartment on the bottom of the panniers). The shower caps work to keep things dry but aren't especially convenient to put on since they're not elasticised. I've thought about making new, elasticised ones but so far have been too busy/lazy.

I leave the panniers mounted on the bike (a thin cable thwarts opportunistic thieves) and shop using my cloth tote bags which, when filled, fit neatly into the panniers. When I get some time, I'm going to build (or perhaps buy, but I'd prefer to build) a front rack for my frankenbike and add 2 more panniers to take care of the occasional heavy-shopping days when I seem to be out of everything all at once.