Why does Battle.net need my phone number?

Your Battle.net account will serve multiple functions, Czinczar, including managing your World of Warcraft accounts (and their corresponding information) and logging into our online Blizzard store. For both of these situations, we ask for a valid phone number so that we may contact you should we have any questions or need to verify a purchase/transaction/etc.

http://us.blizzard.com/en-us/company/about/privacy.html

Q u o t e:
How do we use your personal information?
The personal information you provide Blizzard will allow us to fulfill your product or service order; alert you of new products or services, features, or enhancements; handle/route your customer service or technical support questions or issues; and/or notify you of upgrade opportunities, contests, promotions, or special events and offers. Blizzard may enhance or merge the personal information collected at a Blizzard site with data from third parties. Blizzard may also provide your personal information to other companies or organizations that offer products or services that may be of interest to you. In such cases, we will notify you that the information will be shared and provide you with an opportunity to opt-out.

Lastly, we may use your personal information for internal marketing, profiling, or demographic purposes, so we can adapt our products and services to better suit your needs. We do this to better understand and serve our customers.

Please be advised that personal information submitted by individuals acting solely in a business capacity (e.g., personal information contained in job applicant's resume) is not subject to the uses set forth above or to any other practices stated in this Privacy Policy.

For reference, though, we also asked for this information whenever you set up your World of Warcraft and previous Blizzard account(s).