I'm going to guess that you are talking about American sports, so...
Major league baseball was still in its infancy, but the sport was beginning to thrive. The National League (founded 1876) and the American League (1901) were in the midst of their early rivalry, and some of the stars of the era--pitchers Cy Young, Christy Mathewson, and Walter Johnson; and hitters such as Honus Wagner and Ty Cobb--were beginning to bring fans to the stands and solidify the game as the national sport. Attendance doubled between 1905 and 1920. But it was still the "dead ball" era, and home runs were rare; pitching still dominated. Babe Ruth would make his first appearance in 1914 as a pitcher, but his bat would soon change the face of the game.
College football was very popular, and it dominated the sport long after professional football came into existence. There was some regional professional football being played in the early 20th century, but what is now known as the NFL didn't begin until 1920.
Basketball was the least popular of the three sports, having first gotten started in the 1890s.
Boxing was one of the most popular sports in American during the first two decades of the 20th century and became the "preeminent sport in the United States" between 1920-1940. One of the best and most popular boxers ever, Jack Dempsey, won his first world title in 1919.
By far the most important professional sport in the United States in this decade was baseball. Baseball was the only truly popular professional team sport in the US at this time. Boxing was also very popular, although it was banned in many parts of the US. Finally, horse racing was a major spectator sport in the US at this time. It provided a major legal way to gamble and was popular in large part due to this.
During the 1910s, tennis and golf became more popular for the masses. In addition to these, the major amateur sport of the time was track and field.
Compared to today, the 1910s were not a big time for sports. There were few professional sports and college sports were not nearly as important as they are now.
Baseball was very popular in the early 1900s, and so was skiiing. Boxing and many of the other olympic-style sports were popular. Most of the sports we know today had definitely not come into their own yet in the US, including football and soccer.
There were many sports prominent in America in the 1910's. Much like any decade from when the first professional sports were played, popularity of certain sports rose and fell.
During the 1910's, many sports were just picking up in popularity. The first Indy 500 (NASCAR) was held in April of 1911. Tennis was among the more popular sports, as well as boxing.
In the United States, college football was popular, which paved the way for professional football to pick up in the late teens and early 20's. In the United States as well as Canada, ice hockey was relatively popular, and gaining more fans every year.
Baseball was also a very popular sport, with attendance to major league games rising every year, from about 6,200,000 in 1910 to about 6,600,000 in 1919.
Hope this helps!
The 1910’s lay the foundation for the Golden Age of Sports of the 1920’s. Tennis and track were primarily amateur sports but became public sports rather than solely within the country clubs. Basketball and football were primarily college sports; however their popularity began to grow within the cities. The Indianapolis 500 was first run in 1911, the first Stanley Cup was held in 1917, and first Triple Crown Thoroughbred champion was crowned in 1919. In the beginning of the decade African –American boxer, Jack Johnson, was the heavyweight champion. Boxing was illegal in many states at that time, although its acceptance increased throughout the decade.
Baseball was probably America’s sport during the 1910’s. George Herman "Babe" Ruth rose to fame in the 1910’s hitting a record twenty-nine homers for the -Boston Red Sox in 1919. The 1919 World Series is known as the “Black Sox Scandal” where eight Chicago White Sox Players accepted bribes to throw the Series.
Just want to make a correction... The first Stanley Cup was actually held in 1894, not 1917.