This may well be an open problem, I'm not sure.

In Berger's classification (refined by Simons, Alekseevsky, Bryant,...) of the holonomy representations of irreducible non-symmetric complete simply-connected riemannian manifolds, there are some cases which imply Ricci-flatness: namely, $\mathrm{SU}(n)$ (Calabi-Yau) in dimension $2n$, $\mathrm{Sp}(n)$ (hyperkähler) in dimension $4n$, $G_2$ in dimension $7$ and $\mathrm{Spin}(7)$ in dimension $8$.

A natural question is the converse: whether Ricci-flatness implies a reduction of the holonomy. The other holonomy representations are known not to be Ricci-flat: $\mathrm{Sp}(n)\cdot \mathrm{Sp}(1)$ (quaternionic kähler) is known to be Einstein with nonzero scalar curvature, and in the case of $\mathrm{U}(n)$ in dimension $2n$ (Kähler) it is known that if a Kähler manifold is Ricci-flat then the holonomy is contained in $\mathrm{SU}(n)$, so that it is Calabi-Yau. So the remaining question is whether there exists any Ricci-flat riemannian manifolds with generic holonomy $\mathrm{SO}(n)$ in dimension $n$.

I would like to know the present status of this question and if it's still open what the experts think: do people expect examples of Ricci-flat riemannian manifolds with generic holonomy?

**Bonus question**: How about if the manifold is pseudoriemannian?

**Added**

Thanks to Igor's answer below, here are some further remarks.

The question needs to be refined. The riemannian analogue of the Schwarzschild metric
on $\mathbb{R}^2 \times S^2$ is an example of a complete, simply-connected noncompact Ricci-flat metric with generic holonomy. So the question is about *compact* examples.

In fact, in Berger's 2003 book *A panoramic view of Riemannian geometry* (page 645) one reads at the bottom of the page:

It remains a great mystery that no Ricci flat compact manifolds are known which do not have one of these special holonomy groups.