Every century has thousands of influential artists; a question like this seems to suggest there are a select few that everyone agrees on. And is "artist" defined by the visual arts alone? or by literature and music as well? In the Nineteenth century, some literary artists who had a profound impact include Charles Dickens (whose popular novels featuring the poor and downtrodden of society had a significant impact upon their readers), Charlotte Bronte (whose novel Jane Eyre was very popular and well-respected and has maintained its popularity today as evidenced by the number of feature film versions in existence), and Edgar Allan Poe, whose poetry and short stories are still regarded as some of the best horror masterpieces ever written.
Twentieth century: F. Scott Fitzgerald (a very successful fiction writer whose career nevertheless ended prematurely due to his alcoholism), Pablo Picasso (whose abstract art redefined aesthetics in the painting world), and Alice Walker (who gave voice to the southern African American experience from a fresh feminist perspective).
Twenty-first century: Shepherd Fairey is a graffiti artist whose painted version of a photo of Barack Obama became an iconic image for the 2008 presidential election.