Steel in general is an alloy of carbon and iron, it does contain other elements, some of which are retained from the steel making process, other elements are added to produce specific properties. The more common elements are listed below:

Carbon (C)
Carbon is arguably the most important element in steel, it is essential in steels which have to be hardened by quenching and the degree of carbon controls the hardness and strength of the material.
Manganese (Mn)
Its presence has three main effects, it is a mild de-oxidant acting as a cleanser taking the sulphur and oxygen out of the melt into the slag. It increases the harden ability and tensile strength but decreases ductility. It combines with sulphur to form globular manganese sulphides, essential in free cutting steels for good machinability.
Silicon (Si)
In most commercial steels it is present in a range of 0.05/0.35% and acts as a powerful deoxidiser. It is present in higher contents in Silicon-Manganese Spring Steels and Acid and heat resisting steels.
Sulphur (S)
It is normally regarded as an impurity and has an adverse effect on impact properties when a steel is high in sulphur and low in manganese. The welding qualities of steels with high sulphur is poor. Free cutting steels have sulphur added to improve machinability, usually up to a maximum of 0.35%.
Phosphorus (P)
Although it increases the tensile strength of steel and improves machinability it is usually regarded as an undesirable impurity because of its embrittling effect. Most steels do not exceed 0.05% phosphorus.
Nickel (Ni)
When added to carbon steel in amounts up to 5% it increases the tensile strength, toughness and hardenability without loss of ductility. Often used in combination with other alloying elements, especially chromium and molybdenum. Stainless steels contain between 8% and 14% nickel.
Chromium (Cr)
Increases hardenability and with high carbon improves resistance to abrasion and wear. An essential element in stainless steels and heat resistant steels where contents of up to 30% may be present.
Molybdenum (Mo)
Increases hardenability and reduces the risk of temper brittleness in low alloy steels. It is added to stainless steels to increase their resistance to corrosion and is also used in high speed tool steels.
Tungsten (W)
Is used as the main element in high speed tool steels. After heat treatment the steel maintains its hardness at high temperature making it particularly suitable for cutting tools.
Lead (Pb)
The addition of lead in levels of up to 0.30% improves machinability. Providing the distribution is homogenous it has little effect on the physical properties of the steel, and contrary to popular belief, it does not affect weld ability.
Selenium & Tellurium (Se,Te)
These elements are added to certain steels to improve machinability. In free machining stainless steels a selenium content of 0.15/0.25% is typical. Tellurium levels of 0.03/0.05% are added to leaded free cutting steels to further improve machinability.