During a trip to the US I realised that many Americans have never heard the word cutlery before ... however some have. Where in the English speaking world (and in particular where in the US) is this is a common term for knives, forks and spoons?
In the United States, cutlery is a formal (read: pretentious) word for cutting and peeling implements, that is, knives and paring utensils. I am primarily familiar with it from department store signs, and perhaps the decline of department store shopping contributes to its declining usage, like calling bed and bath goods domestics.
Cutlery in the British sense encompasses all eating and serving utensils, for which most Americans would say silverware or flatware, regardless of shape or material. This usage of silverware sets it apart from other types of -ware which refer to the material (e.g. glassware, plasticware) or the use of the item (e.g. housewares, giftware).
Martha Stewart calls it flatware, and that is good enough for me.