We call a property generic if it holds for almost all problem instances. For linear conic problems, it has been shown in the literature that properties like uniqueness, strict complementarity or nondegeneracy of the optimal solution are generic under the assumption that Slater's condition is fulfilled. The possibility that Slater's condition generically fails has not been excluded. In this paper, we close this gap by proving that Slater's condition is generic in linear conic programs. We also summarize genericity results of other properties and discuss connections among them.