An interesting fact was relayed to me in [another question of mine][1] that  

<Blockquote> If $M$ is any closed manifold with universal cover homeomorphic to $R^n$ for $n>1$ then $\pi_1(M)$ is freely indecomposable. </Blockquote>

What are some other sufficient conditions for the free-indecomposability of a group? Are there any interesting necessary conditions?

  [1]: http://mathoverflow.net/questions/57902/fundamental-groups-of-closed-hyperbolic-3-manifolds-are-freely-indecomposableBlockquote