There are some cases of bio-metallic materials, as hinted at by the comments. But these are relatively small amount of metal.
It's not that there is a lack of metal available. Iron in particular is the fourth most common element in the earth's crust. Most soil that has a reddish color has iron in it. There are several reasons you don't see iron exoskeletons on animals all the time.
Firstly, metallic iron (in chemistry terms, fully reduced, oxidation state 0) has a high energetic cost to create.
Iron is the second most common metal after aluminum on the earth's crust but it's almost entirely present in oxidized states - that's to say: as rust. Most biological iron functions in the +2/+3 oxidation state, which is more similar to rust than metal. Cytochromes and haemoglobin are examples of how iron is more valuable as a chemically active biological agent than a structural agent, using oxidized iron ions as they do. Aluminium, the most common metal on Earth, has relatively little biological activity - one might assume because its redox costs are even higher than iron.
As to why reduced biometal doesn't show up very often, inability of biological systems to deposit reduced (metallic) metals is not one of them. There are cases of admittedly small pieces of reduced metal being produced by biological systems. The Magnetosomes in magnetotactic bacteria are mentioned, but there are also cases of reduced gold being accumulated by microorganisms.
Bone and shell are examples of biomineralization where the proteins depositing the calcium carbonate or other minerals in the material are structured by the proteins to be stronger than they would be as a simple crystal. most of the examples here have very little or no metal, but rather minerals like the Chrysomallon squamiferum cited by @navyguymarko and @loki'sbane here. The Iron Sulfide looks metallic but it is a mineral, akin to a bone.
While iron skeletons might seem to be an advantage, they are electrochemically unstable - oxygen and water will tend to oxidize (rust) them quickly and the organism would have to spend a lot of energy keeping it in working form. Electrical conductivity sounds useful, but the nervous system favors exquisite levels of control over bulk current flow, even in cases like electric eels, whose current is produced by gradients from acetylcholine.
What's more, biological materials actually perform as well as or better than metal when they need to. Spider silk has a greater tensile strength than steel (along the direction of the thread). Mollusk shells are models for tank armor - they are remarkably resistant to puncture and breakage. Bone is durable for most purposes and flexible in addition.
The time it would take for metallized structures to evolve biologically are likely too long. By the time the metalized version of an organ or skeleton got started, the bones, shells and fibers we know probably have a big lead and selective advantage.
