  K-theory and Ext are computed for the C*-algebra C*(E) of any countable
directed graph E. The results generalize the K-theory computations of Raeburn
and Szymanski and the Ext computations of Tomforde for row-finite graphs. As a
consequence, it is shown that if A is a countable {0,1} matrix and E_A is the
graph obtained by viewing A as a vertex matrix, then C*(E_A) is not necessarily
Morita equivalent to the Exel-Laca algebra O_A.
