Shopping in Granada is where most travelers have a type of cultural epiphany. When we think of southern Spain, we see images of multi-colored tile, whitewashed villages, ornate arches, and busy street markets. All of these, however, are more Arabic in tradition than Spanish and nothing showcases this better than Mercado Arabe. This center city market consists of a long stretch of shops specializing in Moroccan-style clothing, bric-a-brac, and fresh spices. The market will be crowded any time you go and that's part of the enjoyment. Float around in the ocean of people for a while and watch how they strike up a bargain!
Granada is an excellent place to buy colorful jarapas (rag rugs), pretty basketware, fragrant spices, and beautifully inlaid wooded boxes. Some of the places selling these boxes are also workshops where you can watch the ancient art of marquetry in progress.
Of course, there are also plenty of shops that deal in modern goods like high fashion and ski gear. If you, like so many travelers, are only visiting for a day trip to the Alhambra, there is a great little shop on the hill next door. It doesn't have the feel of a street market or workshop, but inside is a wide range of excellent souvenirs!
A note on shopping in Andalucia: if you find something you really like, buy it! Shop owners are kind and do not inflate their prices no matter their store location. The only places it pays to shop around are the street markets where haggling is practically encouraged!