Quite many - I would estimate that he did at least ten Sunflower paintings. You can look it up in Ingo Walther's book of the complete paintings by Van Gogh: http://www.amazon.com/Van-Gogh-Complete-Paintings-Klotz/dp/3822850683 The book is easily accessible and quite cheap. I have it at home, too (but just now I am not at home, hence I can't count for you!).

One can make a mental connection between the artists name and painting but also between the artist and their influence on the development of art through these paintings. Vincent van Gogh's Sunflower paintings have been duplicated many times by various artists (although never reaching the vivacity and intensity of Van Gogh's) and displayed everywhere; from households to art expos.Those by van Gogh must be around 12/15. Upon looking at these paintings one begins to notice aspects that seem to flow from one piece to another. The colors are vibrant and express emotions typically associated with the life of sunflowers: bright yellows of the full bloom to arid browns of wilting and death; all of the stages woven through these polar opposites are presented. Perhaps this very technique is what draws one into the painting; the fulfillment of seeing all angles of the spectrum of life and in turn reaching a deeper understanding of how all living things are tied together. There are many pieces within this series of paintings (each is clearly identifiable as a Van Gogh work) in which there are only minor differences that separate them. The overall layout of the painting along with positioning of the actual sunflowers usually remains the same in the similar paintings.

according to Wiki answers 102.. sunflowers.