Is there a lover-of-fine-art on your gift list? Lucky you! This will be one of your easiest purchases and it will make you look extremely thoughtful at the same time. And what's better than that, honestly?
The artist-to-be is super simple to buy for because they don't already have everything and probably haven't even developed preferences yet. So you can surprise them with a full set that includes all they need to get started. Depending on their interest or experience, choose between watercolor, acrylic, or oil paints. Or buy a box of Prismacolor colored pencils with blending tools, a set of oil pastels, a box of chalk or charcoal sticks, a collection of pencils for sketching, or artist markers good for comics and architectural drawing. If that seems too overwhelming, consider signing them up for a local class or workshop where they can dabble and learn more about what they like to do without making the investment in materials first.
Your more experienced artist probably already have a base of supplies and their favorite brands so don't just buy anything in the art section. A lot of what is on the shelves is student-grade, meaning lower quality. You could check out their art box to find out what they use, but it might be hard to know which colors or brushes they need right now. You could just ask them if you're okay with that (perhaps have them circle items in a catalogue), or you could get them a gift certificate to the local art store or for an online retailer like Cheap Joe's, Dick Blick, or Jerry's Artarama. Gift certificates don't usually say "I put time and thought into this gift," but if they are a starving artist, they will absolutely appreciate it and put it to good use. They also might like books by artists or instructional DVDs by artists they admire, or art classes or workshops. If you're feeling adventurous, you could even sign the both of you up for a class in a new medium, and enjoy learning together.
Perhaps you're buying for someone who either doesn't create the art themselves, but loves to look at other's art. A great idea would be to buy them a pass to a local art museum, or tickets to a big art opening. Or if you think they'd rather admire from the comfort of their home, you might purchase a beautiful coffee-table book about a famous museum such as the Louvre, or about their favorite artist.
If you're willing to spend a little more, consider purchasing a print or better yet, a piece of original art. Don't know what they like? Slyly suggest going gallery hopping with them for research purposes. Keep your eyes and ears open. Find out what they love, go back later, and surprise them with how well you listen! If you have too small of a budget to support their hobby by buying original art, give tickets to an art auction as your gift. Go together. They'll leave feeling complimented by your time and interest without you breaking the bank.