Apps that use OpenClip will no longer be able to copy and paste between applications. However, applications can still utilize a persistent way to store data inside the application, meaning that copy and paste within the app will still work fine. And on top of that, apps that utilize only one form (either copy or paste) can disable interface elements when Apple axes OpenClip.
However, even though apple is killing the concept behind the current OpenClip, that doesn't mean we can't change the concept. A shared clipboard could be stored in an Address Book card or even on a remote server. Those solutions aren't as good as the OpenClip implementation, but they aren't bad.
The address book version, would have to write a very weird looking address book card to your address book. It would probably get synced and it would show up on your Mac or PC or even MobileMe. I'm not too cracked up about that, but I would be interested to know what users think of that (email me). The network solution is impossible for Apple to shut down, but it is no easy task. Just ask Apple's MobileMe department.