-Earth has mithril and Westeros has Valyrian steel. While Dungeons & Dragons and its close cousins possess numerous special materials, I'm going to focus on something a little different today: extraordinary materials.
I guess I should define my terms so you can understand what I'm talking about. Extraordinary materials are materials that possess qualities that border on the supernatural. In game terms, this means that weapons crafted from the extraordinary material possess certain abilities equal to magical armor and weapon enchantments.
We'll use Valyrian steel as an example for how to handle extraordinary materials. In game terms, weapons crafted from Valyrian steel would receive the benefits of the keen weapon enchantment due to how sharp weapons made from the material tend to be.
As I mentioned above, extraordinary materials might grant different abilities depending on the type of item being made. For example, there is a rare material known as blue ice that happens to be just as strong and durable as steel. When used for weapons, blue steel grants the benefits of the frost weapon enchantment. However, when the material is used for armor, it grants the wearer a resistance against cold damage.
I've mentioned before that I like magic items that are more unique and mystical. Basically, this is just another attempt to achieve that affect. It also helps add a little more of the fantastical to the game without having to always resort to magic. While you could use this for high magic campaigns, I think would shine best in more low magic settings (especially E6 games if you want to use the d20 system). Just make the materials rare to explain why they aren't showing up everywhere and it gives you adventure hooks.