  The K\"unneth formula is one of the basic tools for computing cohomology. Its
validity for foliated cohomology, that is, for the tangential de Rham
cohomology of a foliated manifold, is investigated. The main difficulty
encountered is the non-Hausdorff nature of the foliated cohomology spaces,
forbidding the completion of the tensor product. The results presented here are
a K\"unneth formula when both factors have Hausdorff foliated cohomology, a
K\"unneth formula when one factor has Hausdorff finite-dimensional foliated
cohomology and a counterexample to an alternative version of the K\"unneth
formula. The proof of the second result involves a right inverse for the
foliated de Rham differential.
