This conductive thread is made for wearables!

It's thin, strong, smooth, and made completely of 316L stainless steel for great conductivity and resistance to corrosion. This Stainless Steel Conductive Thread - 2 Ply, making it a bit thicker than every day polyester or cotton thread but still thin enough to be sewn by hand in medium-eye needles or with a sewing machine that can handle 'heavy' thread.

Because it is strong and smooth, its ideal for any wearable/e-textile project. It also has fairly low resistivity, 16 ohms per foot so you can use it to drive LEDs and other electronic components that use under ~50mA.