For which Calabi-Yau threefolds is SYZ conjecture known to hold? I would like to know for which Calabi-Yau threefolds SYZ conjecture is known to hold. I am aware of works by Gross-Wilson (Borcea-Voisin CY3s) and Ruan (quintic CY3), but they are quite classical works today and I now wonder if there are any more examples of SYZ. Of course, answer depends on what I mean by "SYZ conjecture", so I am happy with SYZ examples at any level. I also wonder what can one conclude from Gross's many works on this subject.  
I am also aware of Auroux's (and his collaborators') work on SYZ for Fano manifolds, but I am mainly interested in CY threefold case. This comment does not exclude any information about their work that might be relevant to CY3 case (I just don't know any relation due to my ignorance). 
Thank you for your information. 
 A: Let me go from the weakest to strongest sense in which the conjecture should
be true.
First, at the purely topological level, it is true for any Calabi-Yau variety
with a toric degeneration whose dual intersection complex is ``simple''.
These notions are part of my program with Bernd Siebert: see our paper
http://arxiv.org/abs/math/0309070 for the definitions of toric degeneration
and simple. In http://arxiv.org/abs/math/0406171 I proved that all
Calabi-Yau varieties arising in the Batyrev-Borisov construction as
complete intersections in toric varieties have such degenerations.
The problem is that Bernd and I have been putting off writing the paper linking
the logarithmic approach to topological fibrations for years now, largely
due to lack of motivation. So there is no reference in the literature yet
for this result. I do hope we will finally complete this paper next year.
Second, at the Lagrangian level, there are the results of W.-D. Ruan you
mentioned. In addition, Castano-Bernard and Matessi in
http://arxiv.org/abs/math/0611139 showed that given an affine three-manifold $B$
with ``simple'' singularities, one can construct a symplectic six-manifold
along with a Lagrangian fibration to $B$. So one can apply this to the case
where $B$ is the intersection complex of a polarized toric degeneration of
Calabi-Yau threefolds. One expects this six-manifold to be symplectomorphic
to a general fibre of the degeneration, but there is no proof of this at the
moment.
Finally, at the special Lagrangian level, I think it is safe to say there
are no known examples on compact non-singular Calabi-Yau threefolds with
non-degenerate metric. There are some examples for non-compact
Calabi-Yau varieties, specifically toric ones, see my paper
http://arxiv.org/abs/math/0012002
