I vote for whatever they used to make Correlle-ware back in the mid twentieth century. I assume it's some kind of ceramic. Whatever it is, it's excellent.
It is, as near as I can determine, completely impossible to scratch with any normal household material (though we've never tried it with a diamond wedding ring). You can cut anything you want on it with any kind of knife you have as many times as you like, no problem. Likewise, we've never encountered anything that can stain it. All the usual suspects (blueberries, turmeric, etc) come right off, even if you leave the dishes sitting unwashed for several days before you get around to them. They're about as easy to clean as glass.
They don't bend or warp out of their original shape over time like stainless.
It's possible to break the stuff, e.g. if it hits at exactly the wrong angle, but everyone in my family is pretty clumsy, and we've been dropping dishes left and right since the seventies, and we still have the majority of our dishes (except for the plastic ones, e.g., Rubbermaid; almost all of those have broken). We've lost a few of the Correlle-ware dishes, but they've survived frequent dropping much better than plastic -- better than steel if you care about retaining the original shape so they stack neatly.