We give four examples of families of orthogonal polynomials for which the coefficients in the recurrence relation satisfy a discrete Painlev�� equation. The first example deals with Freud weights $|x|^��\exp(-|x|^m)$ on the real line, and we repeat Freud's derivation and analysis for the cases $m=2,4,6$. The Freud equations for the recurrence coefficients when $m=4$ corresponds to the discrete Painlev�� I equation. The second example deals with orthogonal polynomials on the unit circle for the weight $\exp(��\cos ��)$. These orthogonal polynomials are important in the theory of random unitary matrices. Periwal and Shevitz have shown that the recurrence coefficients satisfy the discrete Painlev�� II equation. The third example deals with discrete orthogonal polynomials on the positive integers. We show that the recurrence coefficients of generalized Charlier polynomials can be obtained from a solution of the discrete Painlev�� II equation. The fourth example deals with orthogonal polynomials on $\pm q^n$. We consider the discrete $q$-Hermite I polynomials and some discrete $q$-Freud polynomials for which the recurrence ceofficients satisfy a $q$-deformation of discrete Painlev�� I.

33 pages, 3 figures, submitted for the proceedings of the International Conference on Difference Equations, Special Functions, and Applications, Munich, Germany, July 2005. Revision includes an extra section on $q$-orthogonal polynomials