This might not be the answer you are looking for, but if you are really concerned about your privacy on social networks, then you should probably not register on Google or Facebook at all, and you should avoid their services. Chances are they will end up "guessing" your real phone number anyway, since they collect and analyze every possible piece of data that are available to them, either directly or through any third party services. They are everywhere, and everyone and everything is using their services, so today it's really very hard to avoid them completely.
Just to give you a stupid example, even this website (StackExchange) actually loads the jQuery library from Google. Your favorite app might be using Google's or Facebook's services behind the scenes, or might even be bought by them at some point. Another interesting thing to keep in mind is that Gmail is scanning the content of the emails, so what stops them from collecting your personal data from there? Every time you buy something online, the confirmation email will contain your name, your address, etc. And no matter if you use Gmail or not, just sending an email to someone@gmail.com
writing "Hello, I'm John Doe" might be enough for Google to associate your name to your address, IP, and who knows what else.
That's why I gave up worrying about Google knowing my phone number. If I want to use their services, I'll accept that privacy is not an option. If I really wanted serious privacy, I'd have to avoid all of their services completely, which I don't really want to, plus I know it'd be very hard to do.
If you want a temporary phone number, Vidarlo gave you some good tips. You'll probably have to buy a SIM card illegally (without registration) or buy a foreign SIM card online. But remember that, as I said, the fight against Google and Facebook is much more complicated that this.