I've had a cheeses box for years and it's dead handy. We'e gone through phases when a deli meats box worked as well, although these days we don't have as much use for it because the kids get lunch in school.
I do love all the organisation but I don't think anything else in our fridge would really benefit from it (other than boxes of leftovers, but they're temporary).
In our awkward corner dried goods press, I have a big plastic baking box, a carbs box (pasta, rice, cous cous, that sort of thing) and a bottled ingredients box, purely because it's impossible to see what's in the press unless you can take out a whole box at a time. There's also a smaller chocolate spreads box, because we had too many flavours to not box them, but I hope to eat those down to a more easily organised number.
In the crappy little herbs and spices press, there's a box on each shelf so you can take everything out at once, again for easy visibility.
I do love a categorised kitchen.