After starting up, IDEA will not open any file and the Project pane comes up empty.
In the notifications area I can see errors with the Subversion plugin (one of its extension points tries to implement a class). The diagnostic message did not mention which extension point and which class, so my only option was to disable the plugin altogether.
After disabling the plugin, IDEA starts up and seems to work. That said, I am rolling back - not having VCS integration sucks.