Caulking Vertical Seams in Three Piece Shower/Bathtub
This can be a subjective question. Here's how I'd approach it. 


Read the installation manual. It's often spelled out clearly which seams should be caulked and which should (or must) remain uncaulked. Sometimes caulking the wrong place results in leaks or overflow. 
Consider the problem of trapped moisture and mold/mildew. If caulking a seam would result in puddling or extended moisture accumulation, and doens't resolve a drainage problem, it may be worth avoiding. 
Does the caulk joint improve or degrade the aesthetics of the unit? Well-done caulk joints virtually disappear into the structure. Poor ones look amateurish and messy. Can the joint be done well in a given location?


If you decide to caulk a joint, I recommend 100% silicone. Latex-based caulks collect surface soil, shrink considerably, and may not bond as well to non-porous surfaces. Be sure the surface is very clean beforehand.