Stickball
Stickball is similar to baseball. The only difference, as stated in the game's title, is that the ball is hit with a stick rather than a bat. The stick, whether it was a limb from a tree or wooden stake, was a cheaper option than a professionally manufactured baseball bat. This game is still common today, especially in poorer neighborhoods. Leagues also still exist.
Playing Cards
A variety of card games were common in the 1930s, such as "Rummy," "Go Fish" and several variations of "Solitaire," which is a one-person game. The same deck of playing cards could be used for all of these games. Therefore, you did not need to spend much money on specialized decks. However, the game "Snap" required a particular deck. This was a game invented in the 1930s and could not be played with the traditional 15th century design of standard playing cards.
Boardgames
Boardgames use a flat board and game pieces. "Monopoly," a game of money and property, was invented in the 1930s. "Scrabble," a spelling and crossword-style game, was also invented in this era along with "Sorry," a game of chance. These games still exist and have changed little, although, Monopoly has versions geared to cities or other themes.
Yard Games
Yard games often require no equipment -- just a group of players. "Duck Duck Goose" was created in the 1930s as was "Red Rover." :Hopscotch," only requiring chalk and a rock was also a game of the 1930s. All of these are still played today in schoolyards, neighborhood streets and sidewalks.