The new Curve Volume add-on allows for easy mesh deformation.
Curve Volume is an add-on for Blender 2.7x that allows using of a set of bezier splines to define a target volume. Geometry of an input mesh is then transformed to fit the target volume. Primarily, the add-on is intended as a modeling tool, used in cases where a desired general shape of a mesh is best described by spline curves representing its boundaries.
By targeting a shape key data however, it can be used as a tool for the creation of shape key animations. For the simple, single volume deformations, the add-on provides a template curve object which can be quickly adjusted and used to modify an object. For cases where a single volume does not produce a desired result, user can manually create a curve object with multiple volumes.
Please note that not every possible geometry of a single curve volume will result in a perfect output shape. For demanding shapes, it might be necessary to adjust the deform options or to use multiple volumes.