  In this article we prove a general theorem which establishes the existence of
limiting distributions for a wide class of error terms from prime number
theory. As a corollary to our main theorem, we deduce previous results of
Wintner (1935), Rubinstein and Sarnak (1994), and of Ng (2004). In addition, we
establish limiting distribution results for the error term in the prime number
theorem for an automorphic $L$-function, weighted sums of the M\"{o}bius
function, weighted sums of the Liouville function, the sum of the M\"{o}bius
function in an arithmetic progression, and the error term in Chebotarev's
density theorem.
