  Let $f(t_1,\ldots,t_n)$ be a nondegenerate integral quadratic form. We
analyze the asymptotic behavior of the function $D_f(X)$, the number of
integers of absolute value up to $X$ represented by $f$. When $f$ is isotropic
or $n$ is at least $3$, we show that there is a $\delta(f) \in \mathbb{Q} \cap
(0,1)$ such that $D_f(X) \sim \delta(f) X$ and call $\delta(f)$ the density of
$f$. We consider the inverse problem of which densities arise. Our main
technical tool is a Near Hasse Principle: a quadratic form may fail to
represent infinitely many integers that it locally represents, but this set of
exceptions has density $0$ within the set of locally represented integers.
