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Criteria: Influence, contemporary & historical acclaim, initial & lasting popularity

Disclaimer: This list is strongly influenced by the Western canon of art. This means that in the broader scope of a global art history certain regions may be underrepresented, among them Russia, India, China, Africa and Latin America.

1. Michelangelo
2. Pablo Picasso
3. Leonardo da Vinci
4. Rembrandt van Rijn
5. Giotto
6. Jan van Eyck
7. Claude Monet
8. Raphael
9. Paul Cézanne
10. Caravaggio
11. Vincent van Gogh
12. Auguste Rodin
13. Gian Lorenzo Bernini
14. Diego Velázquez
15. Wassily Kandinsky
16. Albrecht Dürer
17. Donatello
18. Édouard Manet
19. J. M. W. Turner
20. Johannes Vermeer
21. Francisco Goya
22. Salvador Dalí
23. Henri Matisse
24. Jackson Pollock
25. Peter Paul Rubens
26. Titian
27. Giorgione
28. Hieronymus Bosch
29. El Greco
30. Hokusai
31. Massaccio
32. Andy Warhol
33. Paul Gauguin
34. Sandro Botticelli
35. Gustav Klimt
36. Edvard Munch
37. Duccio
38. Caspar David Friedrich
39. John Constable
40. Jacques-Louis David
41. Pierre-Auguste Renoir
42. Edgar Degas
43. William Blake
44. Jean-Michel Basquiat
45. Mark Rothko
46. Georges Seurat
47. Eugène Delacroix
48. Théodore Géricault
49. René Magritte
50. Edward Hopper
51. Georgia O'Keeffe
52. Frida Kahlo
53. Giovanni Bellini
54. Kazimir Malevich
55. Henri de Toulouse-Lautrec

I don't know much about the topic, but here in Spain I see Velazquez and Goya much more acclaimed than Picasso.

Obviously you'd know their reputation in Spain better than me but it hardly can be extrapolated on the rest of the world.

Rothko should probably be somewhere in the top 50.

Added.

Tim, are you planning on extending this list to 100?

Would be nice but I kinda forgot of it as of late. Wanna help me out?

Some people who could fill out the last 100
Marcel Duchamp
Constantin Brancusi
John Singer Sargent
Marc Chagall
Diego Rivera
Caspar David Friedrich
Alexander Calder
Mary Cassatt
PIeter Bruegel the Elder
Grant Wood
Roy Liechtenstein
Banksy
Keith Haring
Gustave Courbet
Piet Mondrian
Tintoretto
Andrea Mantegna
Alberto Giacometti
Nicholas Poussini
James Whistler
Rogier van der Weyden
Hans Holbein the Younger
Frans Hals
Jean-Antoine Watteau
Jean-Auguste-Dominique Ingres
Fra Angelico
Paolo Uccello
Utagawa Hiroshige
Winslow Homer
Paul Klee
Egon Schiele
Joan Miro
Henry Moore
Willem de Kooning
Francis Bacon
Georges Braque
Jasper Johns
Henri Cartier-Bresson
Ansel Adams
Helen Frakenthaler
Artemisia Gentileschi
Amadeo Modigliani
Yayoi Kusama
Alexandre Cabanel
Alexandros of Antioch
Thomas Cole
Norman Rockwell
Matthias Grunewald

I could see Botticelli a bit higher.

Suggestion for a placement?

Maybe 34.

Done.