Store them in your medicine cabinet. Use magnetized hooks to stick to the metal backing of the medicine cabinet and hang your necklaces on them. They'll stay clean and dust-free.
If this is not possible, consider something like this from QVC:
This is a jewelry mirrored wall cabinet from QVC. Costs less than $80 and holds a ton of jewelry including necklaces, rings, bracelets and earrings. Plus the inside is lined in a tarnish free fabric to keep all your sterling silver jewelry shiny. I am tempted to get one of these myself!
Click here to get to the QVC page.