Notice to my future self: Recently I wondered why one of the computers doesn’t show the correct time. Among others, there are the following lines in /etc/ntp.conf:
interface ignore eth2 interface ignore eth3
As this computer doesn’t have eth2 and eth3 but only eth0, ntpd assumes that I want to ignore all network devices and just listens on lo. After removing those lines, everything is working fine. The version of the Debian ntp package is 1:4.2.6.p5+dfsg-2+deb7u1 and you can find the bugreport here.