What a fun question!
The list could go on and on but here are a few that I am pretty sure would make anyone’s most famous living artist list. I'll put them down as I think of them in no hierarchy of fame or importance. I apologize in advance for all those great and famous living artists I forgot.
Davis Hockney (born 1937) is considered one of the most influential British artists of the twentieth century.http://www.google.com/images?client=safa
Frank Stella (born 1936) was called the most influential artist of the seventies… still a super star of the art world.http://www.google.com/images?um=1&hl=en&
Don Eddy (born 1944) gained fame as a photo realist; but his recent works have veered into the realm of metaphysics.http://www.google.com/images?um=1&hl=en&
Damien Hirst (born 1965) is the most prominent member of the group known as the Young British Artists (or YBAs), who dominated the art scene in Britain during the 1990s He is internationally renowned, and is reportedly Britain's richest living artist, with his wealth valued at £215m in 2010.http://www.google.com/images?hl=en&safe=
Lucian Freud (born 1922) is always good press. Very well known.http://www.google.com/images?hl=en&safe=
Jenny Saville (born 1970) Famous woman painter:http://www.google.com/images?hl=en&safe=
Yue Minjun (born 1962) is the most famous living contemporary Chinese artist based in Beijing, China. He is best known for oil paintings depicting himself in various settings, frozen in laughter. If you haven’t heard of him yet you will. His piece Execution became the most expensive work ever by a Chinese contemporary artist, when sold in 2007 for £2.9 million pounds (US $5.9 million) at London's Sotheby's.http://www.google.com/images?client=safa
Alex Grey (born 1953) and Alex Pardee (born 1976) are very frequently the subjects of YA questions.http://www.google.com/images?hl=en&safe=
Banksey (born 1974) World’s most famous, anonymous graffiti painterhttp://www.google.com/images?hl=en&safe=
Chuck Close (born 1940) One of my, and everybody Else's’ favorites.http://www.google.com/images?um=1&hl=en&
YA WILL NOT ALLOW ANY MORE LINKS SO YOU'LL HAVE TO LOOK THE REST OF THEM UP YOURSELF ( WELL WORTH THE EFFORT)
Hans Rudolf… H.R. Giger (born 1940) immensely popular Swiss surrealist painter, sculptor, and set designer. He won an Academy Award for Best Achievement for Visual Effects for his design work on the film Alien.
Thomas Kinkade (born 1958) considered as more of a rip-off–artist of schmaltzy kitch, as a legitimate painter, but he is alive and well-known.
Larry Poons (born 1937) To me the lozenges on his paintings make the sound “Poon!” “Poon!” “Poon!”
Barbara Kruger (born 1949), artist and photographer
Edward Ruscha (born 1937), I love his words made into paintings
Tracey Emin (born 1963)
Kenneth Noland (born 1924), I studies with Larry Zox ( passed away) who's work and career resembles Noland
Helen Frankenthaler (born 1928),famous painter married once to super star Robert Motherwell. My sister owns a Frankenthaler.
Christo (born 1935) I almost forgot him and he is more famous than most of the other artists I have already mentioned.
Same thing with Claes Oldenberg (born 1929) and Duane Hanson (opps he died)