At the time of writing it looks like XBMC doesn't have a standalone media server. It's only active while the XBMC UI is running.
As an alternative I've started using Plex, which has the standalone server that I was looking for. The server is managed through a web UI, which also has a player.
Overall I believe Plex is a superior and a more user-friendly solution than XBMC.
- It has player apps for all platforms, plus the web player.
- The apps can play my media even if the device is not on the same network as my server, no VPN necessary.
- My library is accessible and manageable online via app.plex.tv
- My library can be easily shared with and played by other users, like my parents. Each user has their own watched statuses and resume states.
- Library refreshing seems to be more automated and smarter than XBMC.
- It basically lets you build your own Netflix as long as you have an HTPC to host it all with and a good broadband connection.
The only downside is that it's not free, you have to pay for the apps and some premium features like sharing, but it doesn't cost much, and I think it's worth the money.