I realize that baskets don't get much love here, but I've been quite happy with a Wald 585 basket attached to the drive side of my rack with stainless hose clamps. It's held up for about 16 years of commuting and shopping so far. Wald's stuff is kinda stodgy, but quite durable and inexpensive.

On the drive side, it counter-balances my kick stand, so I can load it up without the bike tipping over. This is convenient at the supermarket. At work, it's where I store my helmet and outerwear.