While a lot of vitamin and mineral combo products and other supplements in drugstores are marketed as "healthy hair formulas" or the like, remember that this is more hype than hair. There's little science showing that taking any type of nutritional supplements (as in, orally - not by slathering them on your scalp) has any strong effect on your hair health. However, there are certain vitamins and supplements that have been favorably linked with good hair health in studies.
The most important vitamins for hair loss are the B group (B6, biotin, and folate for slowing loss, and pantothenic acid and niacin for promoting hair growth). You can get B vitamins through diet as well, by eating such foods as beans, peas, carrots, cauliflower, soybeans, bran, nuts, and eggs.
As far as supplements go, the extract of the berries of the saw palmetto shrub and the oil in avocados may slow hair loss and promote hair growth by preventing follicle-killing DHT (dihydrotestosterone) from binding to receptor sites at the hair follicles. These supplements are controversial, however, and there are few studies that show their effectiveness. There is also some evidence that the amino acid L-lysine (at 500 to 1,000 mg) can help hair grow thicker, although this hasn't been tested in humans; sheep grew thicker coats after being given L-lysine, so some speculate that taking the amino acid could make people a bit woollier too.
Find out more about this book:YOU: Being Beautiful: The Owner's Manual to Inner and Outer Beauty