This feature has been introduced in Jupyter Notebook 5.0.
Use pip install notebook --upgrade to upgrade to the latest release.
The old shortcuts C, V and X work only for copying and pasting inside one notebook. In order to do it across tabs, you should use Ctrl-C and Ctrl-V (Cmd-C and Cmd-V on Mac).
Note on multiple cells: currently (jupyter 6.0.0) on Mac+chrome using shift-click to select the cells then cmd-C does NOT work, while using the keyboard with shift-down-arrow does! (thanks drevicko for pointing this out)