Blender Version
Broken: basically since always.

Short description of error
If you use a curve object to deform something, e.g. curve deform modifier or spline IK chain and then use another deform modifier to said curve, the modifications will not get passed on to the children. You can see the deformation of the curve, but the Mesh, or IK chain stays straight. However if you apply the wave modifier the mesh will get deformed, so there must be something with the order in which the modifiers get calculated. I was afraid that that would just be the nature of things, but it works with lattices, so please, please change it, it would open up whole new ways to rig animals.

Exact steps for others to reproduce the error
Add a curve, add a mesh. select mesh, then curve, press crtl p and choose curve deform. select the curve and add a wave modifier. When you scrub through the timeline you will see the curve wave, but not your mesh. (see Blendfile)