Antique bookcases. I do not know what style your interior decoration is, but we buy nice antique bookcases (if it has been used for more than, say 20 years, it turns from 'used' to 'antique' :-) in solid cherry, mahogony, and rosewood with glass fronts. We like good construction and don't mind a few dings and scratches so this works for us.
Expect to pay $400+ for a solid mahogony case with glass doors that would hold ~300 CDs and about $1200+ for a cherry/mahogony one that holds ~1000 CDs and about $1800+ for solid Oak ~1000 CD bookcase (Oak is popular this decade). Find ones that have shelves that can be repositioned so that you can set the heights to CD size.
Expect to pay $400+ for a solid mahogony case with glass doors that would hold ~300 CDs and about $1200+ for a cherry/mahogony one that holds ~1000 CDs and about $1800+ for solid Oak ~1000 CD bookcase (Oak is popular this decade). Find ones that have shelves that can be repositioned so that you can set the heights to CD size.