Even though it was documented that a John Daly played with a wooden ball in 1550, by 1618 the first hand-crafted goose feather golf ball, wrapped in horse or cow hide, was introduced. To make it harder, it was made wet so that the leather shrunk and feathers expanded.
In 1849, the Gutta Percha ball 'Guttie' was introduced by Rev Adam Paterson of St. Andrews, which was made from the rubber-like sap of the gutta tree found in the tropics. The rubber was heated up to be formed into a sphere and could easily be repaired by re-heating it. This ball was not known for traveling as far as the feather ball.
By 1880, Gutties were being produced with patterns on the outside to improve their distance, and by 1890 they were being molded with machines. The most common pattern was the 'Bramble', which had raised bumps around the outside of it. Soon Dunlop and other companies began mass production of balls, which killed any handcrafted ball businesses.
Coburn Haskell introduced the one-piece rubber-cored ball in 1898, which was then used in the British and U.S. opens by 1901 after being proven to be superior by adding 20 yards to a drive. Looking just like Gutties, they had a solid rubber core and were wrapped in thread incased with a gutta percha sphere.
In 1905, William Taylor applied the dimple pattern to the Haskell ball, which maximized lift and minimized drag - and created the first modern golf ball. In 1906 Goodrich introduced the pneumatic ball, which had a compressed air core which tended to expand from heat. Only after others tried cork and metal cores did Spalding introduce the first two-piece Executive ball in 1972.
R&A and USGA in 1921 standardized the weight and size of golf balls. But the two officiating bodies had different regulations, which meant that different sizes were being used in the U.S. and Europe.
Today, there is a wide variety of balls made for certain players or circumstances which offer more control over aspects like distance or spin.