The symptom is that at the login screen I was unable to login as myself, but I could log in as other users or as root.
The problem turned out to be that the root partition (“/”) was full. To solve the problem I logged in as root and went to /var/log/journal/257adc6a3c2544e98cae7eeea8f97e6e and removed the files in the journal.
After rebooting the machine I was again able to login as myself. I noticed that Dropbox, which had been complaining that it was not able to start, is now able to start again.