TITLE: Kähler manifold which is not algebraic
QUESTION [6 upvotes]: Can someone provide examples of Kähler manifolds which are not algebraic?
This question came to my mind seeing the post of Andrea Ferretti.

REPLY [3 votes]: You might want to take a look at this previous MO question.
There, I mentioned Voisin's results disproving Kodaira's conjecture (every Kahler manifold 
is deformation equivalent to a projective manifold).