http://contact.googleapps.com/?&rd=1 and http://support.google.com/adwords/bin/answer.py?hl=en-GB&... for example.
AdWords support is outstanding. As a client getting started with Google advertising, I had a dedicated account manager who set up the entire campaign for me, who would call me back whenever I had any questions I'd email to him and was very intelligent and helpful.
I am not surprised that their free services don't have a phone number to call. Can you imagine providing call-centre support for 400 million Gmail users, or 1 Billion+ Google search users?
Of course, if they want to enter other customer facing businesses like selling hardware or broadband Internet, they will have no choice but to set up call-centres for those departments.