What different frame materials have been used? In response to yet another frame materials question, I thought it might be useful to start with a more answerable question. One answer per material please, with an example of a bicycle frame using that material.
Please use the format I've used in my answer(s) to make it easy to compare materials.
I see no harm in having all 400+ steel alloys listed if someone wants to do that, but &quot;steel&quot; must specifically be low-grade mild steel rather than a specific alloy. Likewise for aluminium, titanium, magnesium and other metals.
For composites, including metal composites, I would again prefer specific examples with details (there's a big difference between steel reinforced concrete and kevlar/polyester composites). I would also love to see weird and wonderful bikes included.
Materials
(ie index to answers. Please update links as you add an answer):
Metals

Aluminum Bikes

Aluminum
Scandium - Aluminium alloy


Steel Bikes

Columbus Steel  (not written yet)
ChromeMoly Steel (not written yet)
Gaspipe Steel
Ishiwata Steel  (not written yet)
Kaisei Steel  (not written yet)
Mild Steel
Reynolds Steel (needs extension)
Tange Steel  (not written yet)
Vitus/Super Vitus Steel  (not written yet)


Titanium
Beryllium
Gold (pure)  (theoretical)
Magnesium (not written yet)

Organic

Bamboo
Bones
Wood Bikes

Carved Wood
Plywood (composite)
Wood (complete frame and bicycle)


Cardboard (not yet written)
(https://bicycles.stackexchange.com/a/44582/20060)**

Composites and Polymers

Carbon Fibre
Flax fiber (90% flax, 10% carbon)
Plastic

Layout Specific

Cables aka Tensegrity or Tensional Integrity
3D Printed (not yet written)
Bones

Density average 1.84 g/cm³ for dry bone.

This would be a pretty bad material for a bike frame, and its quite likely that any bone bike really has a metal core in the middle.



Advantage 


Shock factor, or as part of a costume ("Death rides a Pale Horse")


Disadvantage 


Bones aren't particularly structural by themselves.  A skeleton is made from tendons and cartilage and soft tissues as well.
Durability - bones that dry out get brittle and will snap easily.
Intolerant - A crack could go from a minor hairline to a full break very quickly.