Nothing beats teak for a sleek modern look, but there are some concerns to be aware of when looking at teak for CD storage. Unfinished teak has persistent oils that can leave an oily residue or even damage plastic CD cases. If you are choosing teak, always make sure that the product is finished with a durable varnish or polyurethane.
Pine is a nice "earthy" wood and goes well with heart pine flooring, but be aware that pine, like all softwoods, has a tendency to move with temperature and humidity changes. If your CD storage unit is built to tight tolerances where your CDs only just fit in, you might find them getting stuck on days when the wood swells due to high temperatures or humidity.
Hardwood offer the best option in terms of appearance and stability with very few drawbacks. Cherry, mahogany, walnut, maple and oak are popular choices and are generally available in a wide range of tints to match your decor.
Composite products, meaning a synthetic wood product sandwiched between veneers of hardwood, have the advantage of extreme stability as well as low cost. These are usually found at big box retailers. Often slapped with the label of being cheap, some manufacturers are fighting that image with very durable and attractive pieces that are a good bargain for the price-conscious shopper.