Leather Cord - This is great to use for those heavy necklaces that use stone donuts. Plus, it is attractive enough to be incorporated into part of the bead design with out having to worry about covering it up with beads. Usually you'll find it in 1 and 2 mm sizes and it comes in all kinds of colors, so you don't have to just use brown or black any more. If you are uncomfortable with using leather products, there are also a number of imitation products available today as well.
Waxed Linen Cord - This is often used with macrame designs. It doesn't come in a huge assortment of colors and most often will be found only in black or brown. It is pretty strong since it's waxed. If you want to make long necklaces with heavy beads, this would be a cord to consider.
Hemp - Not that long ago, you could only find hemp available in one boring light tan color. But today, you can find it in black, blue, green, purple, etc. I've even seen it available in craft department of my local department store. This is also good to use with macrame and is pretty strong. It works nicely with large beads and the colors can be coordinated well with polymer clay beads too.
Kevlar - This thread is used to make bullet- proof vests. It's often used in seed beads when weight is a consideration. It is very thin, but only comes in a few colors. Yellow is it's natural color, but I've also seen it in black. Another draw back is that it can't be bleached white.
Believe it or not, this is just s smattering of bead stringing media available for you to use. You can find all kinds of bead stringing supplies from most vendors who sell beads under the Beading Supplies section of this site.

