A space with residually finite fundamental group has the nice property that the $l^2$-betti number can be computed as the limit of the usual betti numbers. Of course, there are other interesting connections.
For example, finite groups, free groups and fundamental groups of $3$-manifolds are residually finite.
My question is: Are there some conditions under which $\pi_1(M)$ is residually finite for a locally symmetric space $M$ ?