I created a mobile phone shopping app a while ago with Hecl, and since it seems to have become fairly popular, I did a second, more polished version that is still very simple to use: ShopList.
I think it’s a good way of utilizing a mobile phone and the web together – you enter the list of things to get in a web page, then the phone fetches that list. Realistically, inputting a long grocery list on a phone would drive you mad, whereas with this application, it’s quite fast, and what’s more, it makes use cases like this possible and simple: I’m going to the store, so my wife creates a list on the web site, and sends me the list id, which I use to fetch the list when I’m at the store.