This French supermarket is a great option for general groceries as well as fresh and baked goods. Carrefour kind of does it all pretty well we think, without breaking the bank!
They stock most international brands as well as their own Carrefour brand, which tends to be really good (and cheap) stuff. The fruit and vegetable selection in the Mall of the Emirates branch is probably one of the biggest in town and is very, very good. And being a French supermarket, the dairy section is humongous.