This paper generalizes a class of projection type methods for monotone variational inequalities to general monotone inclusion. It is shown that when the normal cone operator in projection is replaced by any maximal monotone operator, the resulting method inherits all attractive convergence properties of projection type methods, and allows an adjusting step size rule. Weaker convergence assumption entails an extra projection at each iteration. Moreover, this paper also addresses applications of the resulting method to convex programs and monotone variational inequalities.