Place CDs, DVDs and tapes in old shoe boxes stacked one on top of another. Put the bottom portion of one shoe box on one of its long sides and place a second on top of it. Line the two up exactly and staple the adjoining sides together in each corner, along the leading edge and toward the back -- wherever necessary to create a secure joint between the two adjoining box sides. Decorate the shoe boxes if you want to; cover them in decorative paper, paint them, or cover them in the comics page from the Sunday paper -- whatever you feel makes the boxes look more like a unit instead of two boxes stapled together. Arrange the media inside, separated by small bookends if you have them.
Repurpose other storage for DVDs. Good Housekeeping magazine suggests using a wall-mounted pot lid rack to store magazines and books, and DVD cases could fit in one of these as well. Real Simple magazine recommends hanging plastic shoe organizer bags as storage for arts and crafts supplies; you could use the pockets in one of these to hold media accessories like remotes, ear buds or small personal radios.
Nail pieces of scrap lumber together to form a wooden box, if you truly want something that looks like a home furnishing. Cut four pieces of scrap lumber so that, if they were nailed together to form an open box, the edges of the lumber would extend just a little bit in front of the media. The measurements for your box will vary, dependent on what you want to store. Cut a piece of cardboard to fit one open end of the box and nail it to form a backing.