"The chemistry of it is more like a medieval doctor's prescription than the making of a respectable mineral"

-- John Ruskin (1819-1900)

Ruskin wasn't far off. Tourmaline has a simplified chemical formula of:

XY3Z6(BO3)3Si6O18(O,OH,F)4

Tourmaline, although widely considered to be one mineral, is best described as a solid solution series. The cation sites X, Y and Z in the formula above may be occupied by a wide variety of metal ions. The most common substitutions are:

X: Na+, Ca2+, K+
Y: Al2+, Mg2+, Fe2+, Fe3+, Mn3+, Li+, V2+
Z: Al2+, Mg2+, Fe3+, Mn3+, Cr3+
Now that that bit of ugliness is out of the way, we can take a look at some of the common end members in the tourmaline system. (Please note that the following formulae are ideal end members. As with most minerals that occur in solid solution, the degree of cation replacement will vary throughout the minerals in a rock formation, and even within the crystals themselves.)

Elbaite: Na(Li,Al)3Al6Si6O18(BO3)3(OH)4
Schorl: NaFe3(Al,Fe)6Si6O18(BO3)3(OH)4
Dravite: NaMg3(Al,Fe)6Si6O18(BO3)3(OH)4
Uvite: Ca(Mg,Fe)3Al5MgSi6O18(BO3)3(OH)3

Structure:
Tourmaline belongs to the group of minerals known as cyclosilicates or ring silicates. A tourmaline molecule consists of two overlapping rings. One ring is comprised by six silica tetrahedra, and overtop (or underneath, depending on your perspective) of this lies a second, more complex ring. This second ring has two parts of its own: an inner "core section" (the three Y cations and the anions from the O, OH, F group) and an outer section (the Z cations, which bind to the oxygen atoms in the silica tetrahedra, the X cations and the borate groups).

Occurance:
Tourmaline-group minerals are relatively common. They occur as accessory minerals in many igneous and metamorphic rock suites. The most striking examples of tourmaline crystals, however, are found in pegmatites and greisen, and can often reach several inches in length.


Sources:
Deer, W.A., Howie, R.A. and Zussman, J., The Rock Forming Minerals
Simon & Schuster's Guide to Rocks and Minerals
Amethyst Galleries - http://mineral.galleries.com/minerals/silicate/tourmali.htm