  We calculate the kaon $B$-parameter in quenched lattice QCD at $\beta=6.0$
using Wilson fermions at $\kappa=0.154$ and $0.155$. We use two kinds of
non-local (``smeared'') sources for quark propagators to calculate the matrix
elements between states of definite momentum. The use of smeared sources yields
results with much smaller errors than obtained in previous calculations with
Wilson fermions. By combining results for $\vec p =(0,0,0)$ and $\vec p
=(0,0,1)$, we show that one can carry out the non-perturbative subtraction
necessary to remove the dominant lattice artifacts induced by the chiral
symmetry breaking term in the Wilson action. Our final results are in good
agreement with those obtained using staggered fermions. We also present results
for $B$-parameters of the $\Delta I = 3/2$ part of the electromagnetic penguin
operators, and preliminary results for \bk\ in the presence of two flavors of
dynamical quarks.
