So, things you can do in my game:
Mithril: Pretty much by the RAW except that I retain the Tolkien trait that Mithril is 'true silver', meaning it counts as silver for the purposes of damage reduction.
Adamantium: 'True Iron', and counts as 'cold forged iron' for the purposes of overcoming damage reduction. Largely otherwise by the book except that DR is about halved in my game so its DR overcoming ability is also halved.
Orichalcum: 'True Gold'. At 5% heavier by volume than gold, is generally too heavy to use as equipment, and too expensive and rare to find in quantity. Usually found in parts per million with normal gold and other metals and must be magically separated from it. Gold or copper with even parts per thousand of orichalcum counts as a rich lode. Hard as adamantium but easier to work do to lower melting point and the fact it doesn't crack, but will not take an edge. Naturally magical and so even unenchanted over comes enchantment related DR. Objects can be magically plated with Orichalcum to make them largely immune to alchemical effects including acid and giving them minor SR and improving their ability to overcome magic related DR. Orichalcum plated metal armor confers minor SR, scry resistance and acid resistance, minor enhancements to freedom of action in some circumstances (web spell, for example), and is immune to rust. On the down side, it makes the armor interfere even more with spellcasting and plating adds weight. Even the plating is rare and expensive though, and is as showy as all heck. The Dwarven High Thane has the only orichalcum plated armor I'm aware of in my campaign world. That's how rare the stuff is. It's like vorpal swords. I know they are out there in theory, but good luck ever getting one as a PC.
Galvorn: 'True Tin'. Also from Tolkien. Galvorn is used to make highly pliant metal objects that can be bent without becoming hard. It's roughly the same weight and cost as Mithral but can't form rigid plates without alloying it and thereby losing some of its better qualities. You can weave cloth from galvorn, and although its more interfering with spell casting than normal gear, armor made from galvorn has basically no armor check penalties. It's also night black unlike mithril which pretty much glows. It's not possible to make heavy armor from galvorn though, and in general mithril is your better bet for most purposes. The goblins weave galvorn wires together to form deadly metal whips that can slash through steel. Small amounts of galvorn can be added to copper to create bronze with the properties of superior steel, but this is mostly just showing off.
Dragon Hide: Can be used to create superior hide or scale armor that provides energy resistance. Hide and scales from old dragons can be used to create superior plate with the same qualities.