I know that the Share charm provides a front-end to the new system-wide Share contract, which lets two Metro-style apps share information. What are some specific examples of Metro apps using the share contract?
Windows 8 provides the easiest way to share information across Apps. The system-wide-share-contract can be thought-of as Apps seeing each other as input/output end-points/services.
For instance, you can share photos saved on your SkyDrive thru the Mail App, which supports selecting attachments from SkyDrive.
Using the Charms bar, you could share a Windows Store App with someone by posting a link on Facebook (People App). Or simply save a webpage to OneNote. You could also share news, websites, songs or videos on Facebook (or mail) from the News, IE10, Music or Videos Apps.
There may be lot of other ways - what better way to find out than to explore!