The best gift that you can give an artist is free room and board for a year in a spacious loft studio with track lighting and a generous per diem for expenses.
Something free you can give an artist, and something that would be appreciated, is ATTENTION.
Another free idea is to set up a fan website for them and write reviews of their work.
People are inclined to give art supplies to artists, and no doubt many appreciate this gesture. I love it when the colonel buys me art supplies, because I like to just look at them.
True committed artists can get geeky about their materials, partial to certain types of charcoal or the brand of paint or the kind of found objects they need for their sculptural assemblages. If the artist is particular about materials, consider giving a gift certificate for purchases at the art supply store. The Back-to-School Art Supplies Walk on this site provides contact information for a few good New York stores.
Budding artists of younger ages may be easier to please. I enjoyed flipping through the MetKids catalogue for this year, and knowing that I am immature for my age, I wanted several items for myself.
Many artists also need something nice to wear to openings, because their paint-splattered work clothes are completely embarrassing.
Image: Evidence of a serious art supply addict. Somewhere in Greenwich Village. December 3, 2007.