When in the second half of the 19th century newspapers and illustrated books became popular and widespread thanks to improvements in printing technology, many artists found their base to spread their skills. The official time span of the Golden Age of Illustration is said to be from 1880s to 1920s, but it varied a little bit between Europe and America.
While European illustrators were influenced mostly by the Pre-Raphaelites, Art Nouveau and Post-Impressionists (especially by Les Nabis, a group of Parisian artists), their American colleagues focused around Howard Pyle's Brandywine School of American Illustration in the Brandywine Valley.
Amongst the most popular artists of this time we find Arthur Rackham (UK), Howard Pyle (US), Ivan Bilibin (Russia), Theodor Kittelsen (Norway), Edmund Dulac (France), John Bauer (Sweden), Beatrix Potter (UK), N.C. Wyeth (US), Sulamith Wülfing (Germany) or Florence Harrison (UK, considered also as Pre-Raphaelite). But there were many, many more.
You can see a lot of people strongly inspired or influenced by the Golden Age of Illustration. Alan Lee, for example, or Shirley Barber. The Golden Age illustrations represent many diffrent styles, so everybody can find something interesting and inspirational among them, and yet - despite the diffrences, there's something ephemeral that escapes your senses, but it connects them all.
We also have a lot of fine artists around deviantART, who are visually influenced by those who used to create around 100 years ago - some of their works you could see in this article. Don't forget to check the groups listed below, which are focused around this age, around its specific representants or about illustration in general.