The color change that occurs when iron rusts is evidence of a chemical reaction. A chemical reaction forms new substance(s), and the color change is indicative of a new substance. Some other indications that a chemical reaction has take place are the production of gas bubbles, a solid precipitate forming in solution and heat and light being given off.
Iron undergoes a chemical reaction called oxidation to form rust, or iron oxide. Electrons are transferred from iron to oxygen, causing the iron to be oxidized to Fe3+. It looks very different as an ion in a compound. Most metals oxidize to some extent. Copper forms a turquoise colored oxide and silver forms a black oxide. In both cases you know that a chemical reaction has taken place because of the color change.