Toys are a constant throughout history, throughout cultures. While the average child's toy collection has decreased dramatically, (due to resources, and the fact they shouldn't be goofing off as much) they're still around, especially as Christmas gifts, since there's not much farmwork to get in the way of playtime. Toymakers are their own guild, and the greatest toymakers are found in upstate New York, Canada, New England, and the foothills of the cascades, due the proximity of metals, timber and precision crafting.
Stuffed Animals: Teddy bears remain popular from the industrial age, largely because of their simple design, and the name coming from a former American President (And perhaps the one that most embodies rugged individualism.) For this reason among others, Mickey Mouse is the 20th century cartoon character that has endured the best. Sock monkeys are also more popular than ever, as their knitted and makeshift nature are a natural fit with the scale and economy of the medieval world. Other stuffed animals are popular, but not extensive due to the Americas' lack of megafauna. Because of this, the animism of tribal folklore, and the Industrial age's fascination with mascots and anthropomorphisizing, "plushies" made after non-animal concepts like plants, snowmen, and even fire are very common.
Dolls: "Toy soldiers" remain in vogue, naturally modeled after the pikemen found in the largest empire of America. Most are unpainted, much like the little army men, but one can obtain more elaborate and colorful toy soldier at a premium. If one is especially well-off, one can even find a poseable equivalent to a poseable action figure. Spider-Man is the most popular of such types, because toymakers do not have to do much sculpting of the face--even an amateur parent can probably come up with a Spidey toy. Herdsmen make dolls in their own image, with a small clay or wooden head, but the rest of rawhide and felt. The craftsmanship and exotic novelty even have an appeal to traveling dignitaries and merchants, who try to bring one home for their children, and cowboy dolls are made in this same "floppy" fashion.
Dolls for girls are usually in the shape of children themselves, as care of a doll is seen as practice for rearing children themselves. However, the daughters of nobles will often receive porcelain dolls, some wearing the latest fashion. Dolls called "Barbies" have endured, but they're usually designed with nubile and sexually appealing design, and are definitely not for children. In fact, Barbies are often referenced a shorthand for perverted individuals.
Outdoor toys: Children, and some adults still enjoy athletic endeavors. Whether to play soccer, gridiron, ninepin, or just a game of catch, most balls are leather-bound and wool-stuffed, and generally come in the same shape and size. The focus is on versatility, not specialization. The only specialized ball is marbles, which were popular in the old middle ages, and have made a big comeback. Kites are also very popular, owing in large part to the Benjamin Franklin legend. There are also hula hoops, made from metal or wood.
Vehicles: Toy boats are extremely popular, especially in the communities that inhabit the rivers and coasts. Toy wagons are also pretty common. In areas with a lot snow, toboggans and miniature sleighs are also a "toy", but may sometimes be used for practical purposes. Long gone are the days of toy jets and shiny red firetrucks, but automotive vehicle has curiously remained, if exclusively in toy form; The locomotive. Maybe because it's an icon of the old west, or it being a fixture in popular fantasy stories like "Harry Potter" and "The Polar Express", but toy trains can be a toymaker's pride and joy. They don't circle around the tree or table however--that only happens in fairy tales.