  The orthogonal polynomials $p_n$ satisfy Tur\'an's inequality if
$p_n^2(x)-p_{n-1}(x)p_{n+1}(x)\ge 0$ for $n\ge 1$ and for all $x$ in the
interval of orthogonality. We give general criteria for orthogonal polynomials
to satisfy Tur\'an's inequality. This yields the known results for classical
orthogonal polynomials as well as new results, for example, for the
$q$--ultraspherical polynomials.
