I love my Ortlieb Bike Shopper! Kim and I have each had one for shopping and use around town for almost five years now. One of them started to come apart after a year or so, and it was replaced for free.
It's essentially just a big black bag with a zipper and a zip-loc type closure at the top, so it's waterproof too. There's one zippered pocket inside for keys or whatever, and long shoulder straps for carrying while off the bike.
One of the most convenient things about it, though, is that the clips you use to clip onto the bike can also clip right onto a shopping trolley, as seen here at Marks & Spencer in Marble Arch!