You'll probably see a phone number associated with Hangouts. You can enable or disable this setting: "Help people who have your phone number find and connect with you on Google services, like Hangouts and caller ID by Google." You can edit the phone number, change the way it's verified or remove the number.
There's also a phone number that's used for account recovery. Google encourages users to enable this feature, but it's optional. For now, the account recovery page is not integrated with the account settings page, so it looks different and has a long URL. "We'll use your phone to do things like challenge hijackers or send you a text message to help you access your account if you forget your password," informs Google.
The phone number management page was added back in May, but now it's more functional.
{ Thanks, Herin. }