If your sofa is a medium shade of brown, then your safest bet is to go with another color, as a brown rug (no matter the shade) with a medium brown couch can make a living room feel too warm. But if your couch features an extreme shade of a color (for example, an extremely dark brown or an extremely light brown), pairing with it a brown rug on the other end of the extreme (for example, pairing an extremely dark brown couch with an extremely light brown rug) will add subtle depth while maintaining warm harmony.
For a brown couch, natural-hued pillows like cream, beige, white and tan will work. Keep the pillow colors lighter than the sofa color to create contrast and lighten the feel of brown. Top off with a light throw blanket over the armrest to match the pillows!
Brown leather is similar to brown fabric, except for its shine: leather has a natural luster, so you can choose to bring this out with metallics, or keep the vibe high-contrast by sticking to only matte, dark decorations. For example, a metallic art piece will draw light and help the eye to associate the shine of the sofa with the decor above it, while a matte art piece will add simple, subtle detail to keep all the attention on the sofa itself.