What conditions must we demand for the economy to be always on the saddle path? Is it enough to assume that agents have perfect foresight, or have 'rational' expectations for the economy to always - except in few cases - be in the stable saddle path?

With rational expectations, I think with shocks, there can be a temporary dislocation from the stable path, but then the agents will reoptimize, shifting the economy back to the stable path. 

Are there more situations where this may happen?

Edit: Looking for conditions in the deterministic and stochastic case.
To stick to the simpler deterministic case, it is perfect foresight and the Transvarsality condition (TVC)that guarantees that an optimizing agent will stay on the saddle-path, because all other paths lead to the violation of TVC (corner solutions violate the TVC).  In a deterministic environment and with perfect foresight the agent knows this and so he sticks to the saddle path. The chapter on the basic Ramsey model in Barrow and Sala-i-Martin's Growth  book has a good discussion on the matter.