Presidential china is one of the ways that First Ladies have left their mark on the White House. There is now a special room at the White House (appropriately called the China Room) where pieces from each set are displayed. The plate to the left is from the Wilson set. Not every First Lady has added new china, but many have. The reason for new china every other administration or so is that the sets are used and therefore get broken, stole (yes, this is a big problem! Eleanor Roosevelt actually had some of the plates made larger so that they couldn't easily be put into purses or pockets!), and generally used heavily.
My favorite china is actually the Hayes set, which is displayed to the left. You can see that this china is very color and intricate. Theodore Davis designed these plates and the Haviland company produced them. Davis took designing the china to the next level because he made the plate itself part of his designs.