A post on The Escapist Forums notes that the end-user license agreement for EA's Origin service does not allow users to opt out of having data from their systems collected, and to avoid having your data mined, you must avoid using the service (thanks Joao). Here's the clause in question:

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.

This and all other data provided to EA and/or collected by EA in connection with your installation and use of this Application is collected, used, stored and transmitted in accordance with EA’s Privacy Policy located at www.ea.com. To the extent that anything in this section conflicts with the terms of EA’s Privacy Policy, the terms of the Privacy Policy shall control.