Blood is red in color due to the presence of heme protein.
Blood is red from the protein, hemoglobin. Hemoglobin has a molecule called a "heme" which has the metal iron in it. When the iron is oxygenated, it becomes red. When the iron is deoxygenated, it becomes blue. This is why your veins are blue.
In living mammals, blood is red in color. It is very well known fact. But when we wonder why it is so.... science gives us the answer. Erythrocytes are red in color due to the presence of heme protein. The protein is made up of globin and heme. Heme gives blood cells red color.
Each molecule of heme protein has four heme groups. These heme groups have iron molecules attached to them. They alter their shape and color on interaction with various molecules. Thus heme protein gives bright red color to the blood when it combines with oxygen (oxygenated) and dark red color when oxygen is released.
In vertebrates, arterial blood and capillary blood is bright in color as it is oxygenated, whereas in the veins it is very dark red as they carry deoxygenated blood. The interesting part is, in few molluscs and arthropods, the blood is gray to pale yellow in color but it turns to dark blue when exposed to oxygen in air, as seen when they bleed. This happens due to the presence of copper containing protein in the blood known as hemocyanin. Similarly, the blood in some species of ascidians and tunicates such as sea squirts and sea cucumbers, contains a protein called vanadium. Though its not clear whether they carry oxygen, when their blood gets exposed to oxygen it turns mustard yellow. In order to know the reason for blood being red in color, we need to know more about RBC.