How was gasoline viewed at the beginning of the 20th century?

In 1900, the turn of the century, gasoline was viewed as (at best) a marginally useful product, nowhere near the essential commodity that it is today. At the time, the most important petroleum product was kerosene; Kerosene burns much slower and more consistently than highly volatile gasoline, making it ideal for domestic heating, cooking and lighting in the era before widespread electrification. It was also used as fuel for some steam engines. The process of refining petroleum into kerosene creates gasoline as a byproduct, so refiners were left with large quantities of gasoline that was not particularly valuable.

Gasoline, then, was a cheap, widely available commodity; it was sold by the pint in drugstores, blacksmith shops, and other retailers. It was a mulitpurpose chemical; as /u/3885Khz said, it was widely used as both a solvent and saw limited use as fuel for lanterns, stoves and the like.

However, at the turn of the century gasoline began to gain traction in another application: as fuel for internal-combustion engines. Invented in 1860 by Etienne Lenoir, early internal combustion engines ran on gaseous fuel like naphtha - it was not until the 1876 invention of the carburetor that liquid fuels could be used. In 1886, Karl Benz designed the first automobile, the Patent-Moterwagen, which used a 2/3 hp, single-cylinder engine running on gasoline. By 1894, the Duryea Brothers had built the first automobile in America. However, the automobile and the internal combustion engine were both in their infancy in 1900. The vast majority of Americans had never even seen an automobile, let alone owned one; it was not until the latter half of the 1900s (the decade) that this began to change, and gasoline became a more valuable commodity. The worlds' first gas station, designed specifically to serve automobiles, opened in St. Louis in 1905, and it was not until the mid 19-teens that filling stations became a regular sight.