For an arbitrary transient random walk (S_n)_n≥0 in Z^d, d≥1, we prove a strong law of large numbers for the spatial sum ∑_x∈Z^d f(l(n,x)) of a function f of the local times l(n,x)=∑ⁿ_i=0 II{Si=x}. Particular cases are the number of
 
(a)
visited sites [first considered by Dvoretzky and Erdős (Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp 353–367, 1951)], which corresponds to the function f(i)= II{i≥1};

(b)
α-fold self-intersections of the random walk [studied by Becker and König (J Theor Probab 22:365–374, 2009)], which corresponds to f(i)=i^α;

(c)
sites visited by the random walk exactly j times [considered by Erdős and Taylor (Acta Math Acad Sci Hung 11:137–162, 1960) and Pitt (Proc Am Math Soc 43:195–199, 1974)], where f(i)=II{i=j}.