Section 2 states that unless you tell it not to, it will share your personal information with "third party service providers". Note you have to tell it not to or it will do it automatically:
2. Consent to Collection and Use of Data.
You agree that EA may collect, use, store and transmit technical and related information that identifies your computer (including the Internet Protocol Address), operating system, Application usage (including but not limited to successful installation and/or removal), software, software usage and peripheral hardware, that may be gathered periodically to facilitate the provision of software updates, dynamically served content, product support and other services to you, including online services. EA may also use this information combined with personal information for marketing purposes and to improve our products and services. We may also share that data with our third party service providers in a form that does not personally identify you. IF YOU DO NOT WANT EA TO COLLECT, USE, STORE, TRANSMIT OR DISPLAY THE DATA DESCRIBED IN THIS SECTION, PLEASE DO NOT INSTALL OR USE THE APPLICATION.
Section 3 states that using the software makes you give up your right to privacy, allowing them to monitor your activity: “EA reserves the right to monitor communications on the Application and disclose any information EA deems necessary to (i) ensure your compliance with this License; (ii) satisfy any applicable law, regulation or legal process; (iii) protect the rights, property and interests of EA, its employees or the public. EA also reserves the right to edit, refuse to transfer and/or to remove any information or materials, in whole or in part, in EA’s sole discretion.”
Will this make you think twice about buying Battlefield 3 and Star Wars: The Old Republic?