In a commercial scenario yFiles for HTML certainly provides the required flexibility for drawing organization charts:
There is an organization chart demo online that shows how this can be implemented with the library (which is in fact a general purpose graph drawing library):

The automatic layout algorithms in the library can both deal with purely hierarchic tree structures, but can also deal with "near-tree" structures, where elements can have multiple parents, e.g. to model a management team or multiple parent companies.
The library also has layout algorithms that can deal with generic graphs with arbitrary cyclic complexity and with the edge routing algorithms available, even rare edge cases can be visualized nicely, where edges that do not belong to the strict hierarchical tree-structure can be routed, too (e.g. to indicate an additional layer of relationships) - this is not part of the demo linked above, though, at the time of writing. The more generic layout demo however shows several of the layout algorithms and many of their options in action.
Disclaimer: I work for the company that creates that library, however on SO I do not represent my employer. My comments, thoughts, and answers are my own.