Hi, everyone. I'm new to this great site, and have spent the last couple of hours checking it out.
Joseff is right about using trosion bar suspension. Many F1 teams (Ferrari is one) use torsion bar springing, particularly on the front suspension. The reason for this may actually be less to do with weight, but more to do with compactness of the design. (As an aside, I think Ferrari have even done away with conventional pivots on their front suspension and actually use a flexing joint instead.)
As for the composition of spring components, I don't believe they have to be metal, but cannot be made from brittle materials.
Composite material springs do exist. Chevrolet's Corvette uses a single transverse FIBREGLASS leaf spring, and have for many years. I don't know much about fibreglass, but I wouldn't have thought it a suitable material for springing.
Also, I belive one of the leading manufacturers of carbon brakes has been developing a type of carbon fibre spring