This is one of these questions where it's tempting to just leave it at the title, but let me try to define the objects in question.

A _conical symplectic resolution_ is a projective resolution of singularities $X \to Y$ such that 

* $X$ is algebraically symplectic, 
* $Y$ is affine, and 
* there are compatible $\mathbb{G}_m$-actions on the two varieties which make $Y$ into a cone and act on the symplectic form with positive weight $n$.

Examples include the Springer resolution, a minimal resolution of a rational double point, the Hilbert scheme of points in that space (via the Hilbert-Chow resolution), a hypertoric variety or a Nakajima quiver variety.

All of these spaces have something in common: they are [_Mori dream spaces_](http://en.wikipedia.org/wiki/Mori_dream_space).

Thus, I am inclined to wonder:
> Are all conical symplectic resolutions Mori dream spaces?  Or am I just not original enough to come up with counter examples?