Not sure where you are, but Aldi Süd in Germany is pretty nice. It's not the place to go shopping for specialty foods, of course, but for everyday items, their products are well-priced for decent quality in my experience. In some areas it's even better than that, their cheese selection puts quite a few non-discount supermarkets to shame.

In the US, I really liked Trader Joe's, which seems like an up-market version of Aldi. Which makes sense, seeing as it's owned by Aldi Nord.