Several times per week I hop on the bike and head over to the local supermarket which is about 3/4 of a mile away.  This bag stays in place and out of the way even while I rumble through the fairly rough shortcut I like to take.

It's a small bag, probably one of the smallest you can get, but that's precisely why I got it.  it's not ideal for going to the store but as long as I skip basket and cart and carry all of my items by hand I don't have much trouble fitting it all in.  I did however lose a bunch of organic bananas out of the flap that I had stuffed in there and only partially closed the velcro on.  Someone on the road beside me honked at me as I lost them, but I misinterpreted it as cyclist hate and gave him the finger while I kept riding.  This bag made me a huge jerk!  Negative 10 stars.

True story, but of course I'm kidding and the fault was mine. I'd suggest one of the small or medium sized messenger bags with at least 10-15 liters of volume if you plan to take it to any stores as clearly naught but evil can come of too little bag space in that situation.