How common are abnormal and ugly leg veins?

Very common. The best estimate is that about 25% of the adult population of the United States will develop varicose veins. Of these, varicose veins are nearly twice as likely to occur in women than men (35% vs 18%). They are also more likely to occur as you get older. By the time you are in your 70s, the risk is well over 50% for men and women. At least 80 million american adults have varicose veins.
Veins are common. Both varicose and spider veins are very common and there are reports that 30 to 40 percent of the population may have some form of vein problems. There are varying degrees of vein issues from minor spider veins to extensive varicose veins, venous ulcers and even clots. See a vein specialist for a venous evaluation.