Make It Wider
If you have a long, narrow window in your living room, like the kind found on either side of an entry or other exterior door, keep your window treatment narrow to make the window look wider. Use a curtain that isn't as wide as the window to cover it, so woodwork and a sliver of window peek out the sides. This creates the impression that the window is wider than it actually is, and in the case of an entryway, the window treatments will also make the door a focal point.
If the narrow window is in another part of the room, you can create the illusion that the window is wider by using longer curtain rods and wider curtain panels.
If your narrow window is short or average length, think about skipping the longer curtains for a shorter curtain style such as a valance. Using a valance will keep your window treatment from overpowering the window, and unlike other window treatments, a valance over a narrow window will keep the window's proportions, which may be important if you have more than one narrow window.
If fabric valances aren't your thing, try wooden valances. Wooden valances come in more varieties than typical curtain valances. They can include lights and carvings, for example.
Ditch the Curtains
Consider ditching the curtains altogether in favor of other options, such as blinds. You can have window blinds custom-made, or you may be able to find ready-made blinds in the right size. If you still want curtains, try pairing a narrow panel or two with a roller blind to add depth and interest.