There have been many studies and much written about calcium supplements as well as calcium plus Vitamin D and the amount of calcium in one's diet. There was an excellent review article about these matters recently published in the New England Journal of Medicine (NEJM vol. 369, pp 1537-1543, October 17, 2013) and I thought I would summarize the article here.
First let me say that the interaction between Vitamin D and calcium is not completely understood. It is also not true that calcium supplements can reduce age-related bone loss and the susceptibility to fracture, assuming that one has a diet adequate in the RDA of calcium. (One study did show that taking 800 IU of Vitamin D would achieve this goal.) There is therefore insufficient evidence to recommend calcium supplements in community-dwelling adults.
The RDA of elemental calcium is 1000 mg/day for women up to age 50, and 1200 mg/day thereafter. For men, the RDA is 1000 mg/day up to age 70 and 1200 mg/day thereafter. Most people receive at least this much in their diet. The largest calcium contribution comes from milk and milk products such as yogurt and cheese. The best vegetable for calcium is raw kale, and the best fish is sardines, followed by pink salmon. Another source of calcium is fortified cereals. Diets containing less than 700 mg/day of calcium can lead to bone loss.
The recommended upper limits of ingested calcium is 2500 mg/day in women up to age 50 and 2000 mg/day thereafter. For men The same limits apply at the same ages.
The most common supplements are calcium carbonate (Tums is an example of this) and calcium citrate. Calcium carbonate requires stomach acid to be absorbed, so this pill should be taken with meals, while calcium citrate may be taken at any time. The most common side effect of calcium is constipation and bloating. Some studies show that additional calcium increases your risk of developing kidney stones, and other studies show that it reduces your risk.
It is important to note that bone meal, oyster shells and dolomite may contain lead, and therefore should not be consumed by pregnant women.
There was one study showing that calcium supplements can increase one's risk for prostate cancer, and a larger study showing that it did not. There have been studies showing that calcium supplements increase your cardiovascular risk, as well as studies showing that it does not increase your risk, and there has been a good deal of discussion about these conflicting studies. I generally feel that if you have to argue about the significance of data or a result, then the result is not significant.