I have a blue vein appearing down one side of my face. I amquite a veiny person. This one goes from under my jaw-line to my temple and near my eye. Why could it have appeared?

Normal. This is a common place for a vein to occur and people with lighter/thinner skin tend to show veins more than others.
Normal veins. I agree with drs. Oren and davis. Veins like this are normal and are visible because they are so close to the surface of the skin. If it drives you crazy though, these veins can be often be treated with sclerotherapy and made much less apparent.
Born with it. Prominent facial veins may run in the family. This may be a cosmetic issue for some, and you may seek help by checking out www.Phlebology.Org, and find a phlebologist in your area who can advise you. Some will inject it with a solution (sclerotherapy), and others may remove it (phlebotomy) depending upon the size.