Why is steel the only common carbon alloy?

Actually, IMHO it a question that answers why this disscusion group exists - and remains fundametally yet to be answered.
The word "improve" I think you really mean the ability to adjust the strength of the metal iron - low carbon to high carbon can vary the strength of iron in terms of tensile strength from about 20 ksi to over 300 ksi- several authors have stated this as the greatest dynamic range (or bandwidth) of strength of a single alloy system - quite unique - a known consequent of the quantum theory of solids - but still unexplain from first principles of quantum physics.
Looking at it chemically utilizing a quick look at the periodic table - the only other carbide formers - titanium, chromium, vandium, zirconmium, niobium, some of the rare earths and tungsten (a few other I may have passed up) are too rare or difficult to process. Atomic shells of aluminum, copper, zinc, magnesium, beryllium, lead, bismuth and other metals don't combine with carbon as intermetallics.
The same question can be asked about iron/nitrogen system (nitridng and the more recent high nitrogen steels).
Historically it is more amazing to me that humans have not yet found another alloy system (excluding the stainless steels) with such a bandwidth of strength.
Ed

The fundamentals of steel being the iron atom size relative to the carbon atom, the interstitial space avalable to fit the smaller carbon atom, in both iron's body centered cubic and face centered cubic lattice configurations, and possibility of carbon being available in the form of carbon monoxide and carbon dioxide and the ability to form Fe3C or Fe2C:Fe, and the relative abundance of these elements all contribute to steel's position as a material that can have it's properties "improved by carburizing". There are other atoms near in size to iron in the periodic table that may be of the correct atomic size for interstitial spaces but the lattice structure may be different, no similar compound to Fe3C exists or the material is very expensive.
Mark

Iron is the only one that changes crystal pattern in such a way to make room for carbon to fit into the newly formed "open spaces" when it's heated and then when the iron is cooled will trap(!) the little suckers.
And it isn't just carbon that fits into those spaces, so does boron, phosphorus and nitrogen. Case hardening compounds usually have all those elements avaiable BTW. :)
Iron when heated to a certain temperature switiches from... "body centered cubic" to the "face centered cubic" crystal pattern.
When iron is hot enough to switch to FCC it glows orange hot in the dark and you can feel the heat on your face. ;) (face centerd cubic)
Both crystal patterns, BCC and FCC have the same density tho. :)
The atoms rearrange very slightly but the "open spaces" are distributed differently, see? ...that's all an atom the size of carbon (et.al.) need to get sucked into the open spaces.
Ok, got that? :)
Next, picture a cube made from tinker toys where all the sticks are the same length. It "gives" when pressed from odd angles. Take one stick out and put in the next longer stick. The cube is now under tension (since you hammered it together?;) and doesn't give so easy.
That's symbolizes the distortion created by a trapped C, B, P or N when the iron returns to room temperature and its usual BCC configuration.
Got that one too? ;)
But a cool one anyway. :)
"Metallurgy Theory and Practice" by Dell K. Allen
Alvin in AZ ps- I'm the dumbest guy on s.e.m and so, best qualified to answer the clueless questions. :) pps- BBC iron is magnetic and FCC iron ain't, so, the iron tells you when it's "hot enough".

=2E.. This question is very interesting and although some of the answers already have been given I would like to clearify a few things.
It seems clear the question is about strength, why carbon can increase the strength of iron but not any other metal.
The main reason for this is that iron has two different crystalline forms, BCC (bodycentered cubic) at low temperature and FCC (face centered cubic) above 911 =B0C. Although FCC is actually more closepacked than BCC it has larger interstitial places where the carbon can dissolve and the solubility in FCC is about 2 mass%, in BCC it is less than 0.02 mass%. Iron with more than 2 mass% carbon is not called steel but is used as "cast iron" because its low melting point and although it is very hard is its also very brittle.
Carburizing steel is usually made above 911 =B0C to obtain a high carbon content in the FCC phase (also known as autenite). For plain carbon steels the maximum hardness one can achive is for a little less than 0.8 mass% carbon.
The strength of the steel depend on the cooling from the high temperature. That is the secret of the blacksmiths in the old times. If the iron is cooled slowly it will not be particularly hard because the austenite transforms to BCC (also known as ferrite) and another phase called cementite with the stoichiometry Fe3C. But if the hot austenite is quenched in water (or with more modern techniques in oil) the rapid cooling prevents the normal transformation and a metastable phase called martensite is formed. This martensite is very hard because the carbon atoms trapped inside the crystal lattice prevents the deformation. In order to have some ductility the quenched steel is usually "tempered" at 300-400 =B0C for a short time which reduces the hardness but decreases the risk that the sword, or whatever the blacksmith is making, breaks when you hit a stone for example. If one tempers the steel too long one obtains ferrite and cementite as with slow cooling and a rather soft steel.
When the steel is at high temperure it is soft and can be easily formed and the cycle heating+queching+tempering can be repeated as many times as is needed to form the steel to the desired product and hardness.
Incidentally ferrite is only ferromagnetic to 770=B0C so the dissaperance of magnetic properties is not a criteria of the ferrite to austenite transition.
Other alloying additions like Cr to obtain stainless steels usually decreases the strength and makes the processing more difficult as other phases may also appear.
Bosse