For storage in the kitchen, and a different one for the entry and another for her office, I made 2 thin frames and stapled the wire so it was sandwiched between them. All of the frames were alder stained or distressed to match the decor of each room. You can also simply staple the wire to an existing frame for a more casual look.
Other ideas:
A place to dry artist's brushes and craft supplies
A tool rack
Cut to fit a planter and placed on top of the filler so your stems stay put
On top of a trellis or pergola so your vines don't climb through
Replace the doors of an armoire to create an open curio