Hi there,

is there a way to receive notifications via network (like Growl on OS X or snarl on Windows)?

Background:
My router runs linux, handles telephone, too, and sends notifications to specified devices to show a who-is-calling-notification. This works with OS X, OpenELEC/Kodi, and Windows, but I didn't find a way to send a notification to my KDE system.

You're looking for some sort of daemon that listen on a tcp or udp port and forwards the input to the freedesktop notification protocol. Such should not be very hard to achieve (binding netcat to qdbus might do), but one would require to know the protocol your router/modem speaks (ie. what data is sent to which -very likely- UDP port)

My router executes a custom shell script. So I can do whatever I want. I've already implemented several notification protocols on the "server" side. Kodi's JSONRPC, Growl's GNTP, Snarl's SNP. I wonder if there's already a daemon for KDE, that I can send network-notification-commands to.

KDE implements the freedesktop notification dameon, http://www.galago-project.org/specs/notification/0.9/
That's a local thing and does not listen to tcp/udp sockets.

As mentioned, you could use netcat to wire UDP broadcasts to eg. "kdialog --passivepopup" (the notification spec unfortunately includes a useless variant map, what makes using qdbus tricky)

The good part is that this should work with about every major desktop environment.