What sports were played in the 1940's?
Assuming that you are talking about the United States, by far the biggest sport in that decade was baseball. Baseball was still the "national pastime" of the country and was played and watched by more people than any other sport.
Comparing the '40s with today, basketball was much less popular both on the college and professional levels. Football was popular as a high school and college sport but the NFL was not the dominant league that it is now.
A sport that was popular in those days (both for spectators and for participants) but has declined in modern times was boxing. Boxing was still a major sport in those days whereas it is a fringe sport with very few American stars today.
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Throughout most of the 20th century, baseball was the most popular sport in the United States. In almost every single household there were fans of a certain team, player, or just the sport in general. Many kids had baseball cards of their favorite players, along with memorabilia in their rooms.
College football was also a relatively popular sport. Football was just starting to pick up in popularity in the 40's and 50's, starting with high school and college. It wasn't until about the late 60's and 70's that professional football picked up in popularity (one of the reasons was because the first Super Bowl was played in 1967) to become the giant that it is today.