Do all veins carry oxygen-rich blood?

In the human body, blood is normally carried by veins carrying deoxygenated blood and oxygenated by arteries.

The pulmonary veins, which carry oxygenated blood from the lungs to the left atrium or auricle, and the pulmonary arteries, which emerge from the pulmonary trunk artery and carry deoxygenated blood from the right ventricle to the lungs for oxygenation, are the exceptions.

In fact, deoxygenated blood returns to the heart through nearly all veins. I say nearly because there is an exception when discussing fetal circulation.

The umbilical artery returns deoxygenated blood, and the cycle begins again. In fetal circulation, the umbilical vein transports oxygenated blood from the placenta to the fetal heart.

No, not all veins carry blood that is rich in oxygen; in fact, blood that is returned to the heart from the rest of the body usually contains less oxygen than blood that is carried away from the lungs.