The majority of coffee mugs people use are made out of porcelain or china. This is a good material for making mugs, as it is strong and has a high melting point, meaning it does not break when hot water is added to it. It is also a relatively good insulator, so the heat of the drink is maintained longer. The advantage from a commercial aspect is that it is cheap to produce because a mug mold can be used countless numbers of times to make identical mugs. It is also easy to paint, so a range of colors and designs can be produced, still using the same mold.
Enamel mugs are never entirely enamel, but are a mix of powdered glass on metal or ceramics. This is done to create a high-gloss finish on products such as coffee mugs. The enameling process gives the mug an extra distinct property: it is corrosion-, scratch- and shatter-resistant. In the home, this is not always a necessity, but is very useful in mugs for camping or the military.
Plastic is used for many products in the modern world, and can be used to make mugs for small children or, like enamel, for camping holidays or other situations where breakage is a possibility. Plastics are man-made fibers that cannot be smashed like ceramics and, as they are not metallic, there is no risk of corrosion. The only drawback for plastics is they are not very good insulators, so the heat of the drink tends to be lost more quickly.
Steel, more specifically stainless steel, was once regularly used to make break-proof mugs, but is now more commonly used to make thermal mugs. Stainless steel is iron mixed with carbon and chromium. This makes the material corrosion resistant, unbreakable and gives an attractive luster to the metal. Steel is a very good insulator, so when it is combined with an inner steel layer with air in between, it can keep a drink hot for long periods of time.
Initially, glass may not seem like a good material for hot drinks mugs, as glass can shatter when heat is added. But glass mugs are often treated glass, so they do not have this property. The only issue with glass mugs is that insulation is not as good, so the heat of the drink escapes through the mug itself. Glass is also not as strong as ceramics, enamel or steel, but the heat treatment helps reduce the risk of breakage.