This answer assumes:
- VBox extension pack is installed and current.
- VBox guest additions are installed and current.
There is a suggestion in the comments to downgrade the guest additions in order to get the shared clipboard working. Although that may work, I solved this by taking the opposite approach. Unfortunately, if you're dealing with a new version of Virtualbox, full guest support may not quite be available. You can actually download and install guest additions that are newer than the bundled or released version.
Head to VirtualBox test builds, and in the top table, you will find the latest version of the guest additions. Compare your revision with the version listed, if it's newer simply download and install it.
If all else fails, uninstall the guest additions and reinstall them.
Windows Guest: Control Panel
Linux Guest: sh ./VBoxLinuxAdditions.run uninstall
The guest additions are specifically what provide shared clipboard support. Take a look at the virtualbox documentation to learn what other functionality they provide.