There are tons and tons of use cases for sharing code between server and client. Why would you want to write things twice? The only reason it is not more common is that programming is generally done in different languages on the server and client.

I built an ebook reader that can process ebooks in javascript. Because IE does not support the File API the server needs to pick up the slack when users are on that browser. Sharing code means I don't need to program two versions and I only have to patch bugs once.

It's also common to share validation code. This allows you to check data client-side and then again once it reaches the server using the same code.