My favorite bag is my $15 canvas backpack from the army surplus store. Mine has funny straps that are kind of a pain to open/close, but I realized after I bought it they had the same bag with the easy snap ones. It's pretty enormous (I can fit 3 weeks worth of groceries in it), has padded straps, and hasn't made my shoulder hurt yet. It's meant for war so I'm sure it can survive bike riding. The only problem is it isn't water-proof, but I never usually need it to be.