http://osf1.gmu.edu/~bbishop1/CHEM%20814-579%20Stereochemistry%20Lecture%20slides.pdf
Everything you ever wanted to know about stereoisomerism.
Quick answer: Any reasonably tetrahedral atom bearing four different groups (including isotopic substitution and unbonded orbitals) is a chiral center. However, pairs of enantiomeric chiral centers in a molecule can cancel (meso-compounds. Tartaric acid has three stereoisomers).
Technical answer: Any center (need not contain an atom - helicenes) that lacks all ${S_n}$ symmetries is a chiral center. Any molecule that lacks all ${S_n}$ symmetries is chiral. Consider methyl phenyl sulfoxide and that sulfur's lone pair.
Rigorous answer (Michel Petitjohn, J. Math. Phys. 40, 4587 (1999) et al.): Any collection of anonymous unit mass countable points that sum to finite principle moments of inertia, in any number of dimensions greater than zero, that cannot be superposed upon its mirror image (one coordinate with all reversed signs) strictly by translations and rotations, is chiral. An infinite number ($\ce{Aleph_0}$) of points in a hyperbolic tiling qualifies. Petitjohn's QCM software quantitatively calculates geometric chirality.
That last one is important. It is a recipe for creating an acyclic, undistorted tetrahedral carbon atom bearing four rigorously identical, freely rotating subtsituents that is a chiral center. Planar $\ce{sp^2}$ carbons can be chiral. It demonstrates that no organic nomenclature for chirality can be complete. It demonstrates that at least one physics founding postulate describing vacuum symmetries can be testably defective, measurably empirically falsified by chemical constructs.
The philosophical 900 lb gorillas,
Symmetry Through the Eyes of a Chemist Magdolna Hargittai, István Hargittai, 2009
Fearful Symmetry: Is God a Geometer? Ian Stewart, Martin Golubitsky, 2011.