Playgrounds have their roots in the 19th c. they arose due to numerous contributing factors, chiefly increasing urbanisation and the need to set aside spaces for recreation and an increasing understanding of child development with an emphasis on physical health.

http://www.reddit.com/r/AskHistorians/comments/1cve2p/when_did_playgrounds_first_appear/

Here's a good article on children's games and toys in ancient Greece to give you some idea of the similarities and differences between then and today.

http://hoodmuseum.dartmouth.edu/exhibitions/coa/re_high_games.html