The headphone output on my HP ProBook 6450b on Ubuntu Linux stopped working a few updates ago and I think I’ve found how to fix it:

cd /usr/share/pulseaudio/alsa-mixer/paths
sudo cp analog-output-headphones.conf analog-output-headphones.bak
gksudo emacs analog-output-headphones.conf

Turn on the master volume (it was ‘mute’):

[Element Master]
switched = on

and turn on Speaker+LO:

[Element Speaker+LO]
switch = on
volume = merge

Save and exit. Then restart also with sudo alsa force-reload. Then remove headphones and re-plug them, That should work :)