Hmmm....
I've been pondering this question for quite a while only to come up with the cliched answer that it is because veins carry deoxygenated blood and on coming into contact with the air and becoming oxidised is when we see the red blood.
WRONG!
Well, it is a fact that blood is red regardless of it being oxygenated or deoxygenated. So are we just seeing things? Well to an extend it is what we are seeing. (highlight on the pun here!)
There are many factors in giving veins their blue appearance, it depends on:
1. the scattering and absorption characteristics of blood at different wavelengths of light
2. the oxygenation state of blood which affects it's absorption properties
3. the diameter and the depth of the vessels
4. our individual visual perception
SOURCES:
http://www.imt.liu.se/edu/courses/TBMT36/pdf/blue.pdf