Same stripes, different color family. Often a fabric pattern comes in several different color groups. If you can track down the fabric, an easy way to pick pillows for your striped sofa is to have them made from the same print in a contrasting hue.
Lots of white. Just as with floral upholstery, if you have a bold stripe that is threatening to overwhelm your room, try whiting it out with crisp white walls and white slipcovered furniture.
Neutrals with texture, blue and red. Grass cloth wallpaper and burlap shades add texture and warmth, helping a redbrick fireplace settle into the space. Wood furniture close to the darkest tones in the brick also helps. Larger amounts of blue in a rug and pillows, and just a dash of red, make for a classic nautical look.