Similar to collecting baseball cards, Pokemon, or comic books. Does this happen a lot throughout history or is this a more recent trend? If so what types of toys were collected by kids?
Toy soldiers seem to be the first collectible toy. Soldier figurines have been recovered from several Egyptian tombs. Several noble families from the renaissance era have records of princes having toy soldiers. But toys have been too expensive for most people to collect for most of history. German craftsmen began casting tin soldiers by about 1730. This made the toys cheap enough that a common household could afford to buy them as a set. The military exploits of Frederick the Great and later Napoleon Bonaparte made collection of the toys popular.
Depending on how you define "common" you are looking at the mid to late 18th century or early 19th century.
Porcelain dolls with doll houses became popular in the early 19th century for girls.