If you are talking about the United States, all the same sports were played then that are played now. The only real difference is that some sports were more popular then than they are now and some are more popular now than they were then.
- In those days, baseball was the most popular of the team sports. Nowadays, football has clearly taken over that position, at least in terms of what people like most to watch.
- In those days, boxing and horse racing were really major sports. Nowadays, neither of these is anywhere near to what it used to be.
- Golf and tennis were more of rich people's sports than they are now -- they get much more participation today.
- Soccer is mcuh more important now -- it was played in those days, but not as much as now by any means.
- Finally, basketball has become much more of an important sport now both in terms of playing and watching.
So overall, I would say, the same sports were played back then, but baseball, boxing, and horse racing were much more important in those days than they are now.