We provide examples of groups which are indecomposable by direct product, and more generally which are uniquely decomposable as direct products of indecomposable groups. Examples include Coxeter groups, for which we give an alternative approach to recent results of L. Paris. For a finitely generated linear group Γ, we establish an upper bound on the number of factors of which Γ can be the direct product. If moreover Γ has a finite centre or a finite abelianization, it follows that Γ is uniquely decomposable as direct product of indecomposable groups.