You probably learned your basic human anatomy sometime around grade school. Textbooks said your blood was red and a scraped knee on the playground confirmed it. We bleed red because of hemoglobin, an iron-containing protein that carries oxygen throughout the body. Hemoglobin is comprised of iron, which oxidizes as red like rust, causing our blood to be bright red when oxygen rich. So...

Why Are My Blood Veins Blue?

Well, they're not. They're a dirty red. Of course, the darker blood won't be as dark outside of the body because it will oxidize when hitting air, but it still contains waste from cells. Seeing a vein as blue through the skin is because of the layer just below the epidermis and dermis, the two outer layers of skin. Because our skin's "job" is to protect our bodies from the sun, this provides an interference for how light penetrates the skin by allowing only lower frequency light through, and color is light bounced off of an object, after all. The wavelengths that do make it through to the veins are high-energy blue.

Because of diagrams like this one and medical charts using blue for the contrast of arteries and veins, it has become a common misconception that the blood in veins is blue. Even some of my science teachers have previously said that blood from veins is blue before it hits air... where instantly it's changed to bright red. Seen under vacuum conditions, this has been disproved. For more information about blood: Wikipedia Entry on Blood   Image from www.kidshealth.org

 
While there are creatures out there with blue blood, humans are not one of them. Horseshoe crabs, skinks, and octopi all have haemocyanins, which are clear before oxidization, and blue after binding oxygen to their copper composition.