It is known that every closed oriented 3-manifold is homology cobordant to a hyperbolic 3-manifold. By contrast we show that many homology cobordism classes contain no Seifert fibered 3-manifold. This is accomplished by determining the isomorphism type of the rational cohomology ring of all Seifert fibered 3-manifolds with no 2-torsion in their first homology. Then we exhibit families of examples of 3-manifolds (obtained by surgery on links), with fixed linking form and cohomology ring, that are not homology cobordant to any Seifert fibered space, These are shown to represent distinct homology cobordism classes using higher Massey products and Milnor's µinvariants for links. 2; while • if β 1 (M ) is even, the rational cohomology ring of M is isomorphic to that of # β 1 (M ) (S 1 ×S 2 ).Corollary 1.2. Under the hypotheses of Theorem 1.1, if β 1 (M ) is odd and at least 3 then for any non-zero α ∈ H 1 (M ; Q) there exists β ∈ H 1 (M ; Q) such that α ∪ β = 0. If β 1 (M ) is even then, for any α, β ∈ H 1 (M ; Q), α ∪ β = 0.