If you look at sports from a local, community level, they became more important to the daily fabric of life. Radios were still common in most households, and listening to baseball games broadcast over them, were of course, free. It was not uncommon to find whole families clustered around the radio on Sunday afternoons listening to the Yankees play the Red Sox.
Any kid could play baseball on any streetcorner or field, using shirts for bases, a stick and a homemade baseball to get a pickup game going. The Civilian Conservation Corps and Works Progress Administration had small components of those programs that paid local citizens to organize sports leagues and events. My Grandmother was one of those working for the CCC to organize swim meets.
Sports were an escape in the 1930s for a population that had very little money, little entertainment, less hope and almost no good economic news. For three hours on a weekend, they could be part of the national pastime instead.
If you are talking about sports in the United States during this time, sports was a very big deal in those days, just as it is today. However, the hierarchy of what sports were big deals back then was a bit different than it is today.
First of all, baseball still ruled the US sports scene. You have to remember that in these days, baseball was segregated so there were the white leagues (what we now call the Major Leagues) and there was the Negro League.)
Second, college football was much, much bigger than the NFL during those days. The NFL did exist, but college football was way more popular.
Third, basketball was really not very popular as a spectator sport in those days. The NCAA tournament, which is such a big thing now, was not even created until 1939. The NBA did not exist yet either.
Finally, boxing was a much bigger deal in those days, as was horse racing.
The Depression took its toll on sports during the 1930's. Baseball was very popular and because many people had little or no money there was a major drop in ticket sales. In addition, salaries as well as rosters were cut. Upkeep of ballparks came to a halt. There just was not money available for renovations and upkeep. The Works Progress Administration did provide money for neighborhood sporting facilities.
Promoters were looking for ways to get more people to attend games so sports became more commercialized. Night baseball and all-star games became popular. Race tracks also introduced the "daily double."
Radio also had an impact on 1930's sports. People were able to listen to events such as boxing and horse racing right from the comfort of their own homes.
In the United States (and even many countries around the world), the 1930's were a very difficult time. A majority of families didn't have enough money to feed their children 3 meals a day, and sometimes not even that much. As a consequence, all college and professional sports took a huge blow, with ticket sales, merchandise sales, stocks in the team, etc, all dropping drastically. That being said, people still enjoyed sports.
Baseball was probably the most popular sport of the 1930's. If people couldn't see a game professionally, many just played themselves with everything from real bats and balls to simple sticks and rocks. Football was also a recognized sport, though it was not as popular as baseball. College football was also more popular than the slowly growing professional league.
Hope this helps!