C++ and C are still relevant for games and graphic apps (either 2d or 3d), so it's good to know them if you want to move into that field in general. They're not so relevant for the web, though.

On the other hand, I agree that Java and C# are more than enough for everyday "business" use. They are still much more robust than higher-level languages such as Python and Excel/VBA for business tasks.

You can now use C++ to write Flash games though... Adobe came up with something called "Alchemy" that can compile C/C++ code into Flash, so you can run Quake (1) to run on a browser, or Doom/Heretic/Hexen. Very neat. If Alchemy becomes commonplace, I would expect to see game companies using this technology to target games to Flash and other devices at the same time (e.g. handhelds, iPhone), and that would mean that the language would be C++.