Google does, in fact, have a customer support line: 866-2GOOGLE. However, this line is intended primarily for AdWords, and encourages all other questions to be handled online (somehow that doesn’t surprise me).
One thing that happened sometime earlier this year is that Google stopped personally supporting most AdWords accounts. So if you call in, indicate you are calling about AdWords help, and put in your account number – chances are you’ll get a message that will tell you they no longer offer personal support, to go online to find your answers in the AdWords online support.
However – if you have certain elements meeting a particular criteria in your account, you can still get personal support. From what I’ve been able to find out from Google, this criteria is based primarily on ad expenditure. That is to say – Google takes care of their big spenders, the advertisers who in turn take care of Google. By giving them a ton of money.
This is not the happiest of news for all AdWords users, but hopefully it does clear things up. As far as I can tell, if you have an AdWords Client Center account set up (have Google AdWords Qualification, etc.), they will also offer support. I do not know if this is purely because you have that type of an account or because you are in charge of so many clients that spend a combined amount above their “trigger” figure. I personally am able to get through to customer service, for one of these reasons or the other.
To sum it up – if you want Google support for AdWords, your best bet (unless you’re spending thousands a month or have a Client Center account) is to just go to their support center online, the AdWords Help Center. They do have a lot of information there that covers most topics, so for the most part this is a great resource. Although, admittedly, not as nice (for some people) as being able to just ask someone to help you out in real-time. But you can ask through their contact forms online, if you can’t find your solution in their help center.