The 1930s is typically associated with the stock market crash of October 1929 and the beginning of the Great Depression. Even with the economy doing poorly and conflict building throughout the world, children found games and toys with which to play. Some were more popular than others, but the 1930s saw development of many new toys and games for children.
In the time before electronics reached their current level of sophistication, board games were extremely popular as a form of entertainment. The 1930s saw the debut of three games that are quite popular as of 2011: Monopoly, Sorry and Scrabble. Scrabble took the longest to get a foothold -- roughly five years. Monopoly, however, with it's iconic figure sporting the top hat and cane -- based on the popular image of the robber barons -- and pieces based on famous industries, was an immediate success.
A lot of games that children play in 2011 have been with us since the 1930s, but many have been with us longer. For instance, hopscotch was still a popular game as long as chalk and a hard surface on which to draw were available. Other games -- like hide and seek, duck-duck-goose and even variants of red rover -- were around during the 1930s.
The modern deck of cards -- originating from a 15th-century French design -- has been popular for many years. There were card games in the 1930s that people of all ages could play, not just children. Games like Go Fish, Gin Rummy and even several versions of Solitaire, with multiple card draws and rules for winning, were options. There were also card games like Snap, invented in the 1930s, which required a special deck of cards.
Given the right equipment, which was often improvised based on whatever materials were handy, children could play stickball -- a version of baseball in which players used a stick instead of a bat. Football was also coming into its own in the 1930s and could be played either as a tag version or a full contact game.