Vegetarians and vegans should pay special attention to ensure that they get adequate calcium, iron, zinc, and vitamins B12 and D. Vitamin B12 is very important because it can only be found in animal based products. A deficiency can lead to megaloblastic anemia, and can cause further neurological damage in the future if deficiency is prolonged.
If you are vegan, you should supplement with B12 since you are not consuming any animal products. Vegetarians may need to supplement if their diet is low in eggs. Dr. Goglia already recommends a multi-vitamin and multi-mineral complex of calcium, magnesium, and zinc citrate with vitamin D to keep you functioning at your best.
Be sure to check with your physician about your iron levels to see if you are at risk for iron deficiency since supplementing with iron pills can cause adverse side effects.