I decided to put this here just as much as a reminder to myself as for the benefit of others. :-)
Every time I'm setting up a Raspberry Pi and I want to connect it to my VPN, I run in to this issue. Everything works, WLAN is set up and working, I add my OpenVPN config and... the WiFi on my Raspberry Pi dies.
Here's the solution. Edit the file /etc/default/ifplugd and change this line:
It seems that when set to Raspbian's default "all", the hotplug system tries to manage the VPNs tun0 device, which causes trouble.