A user over on The Escapist Forums has read over the end-user license agreement for EA's Origin, and has found that the service doesn't allow users to opt out of system information collection, nor data mining.
According to the Consent to Collection and Use of Data clause in the EULA, in order to avoid having your data collected by EA, you simply refrain from installing the service.
Here is the clause causing concern:
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.
Note, that the clause doesn't say EA will be collecting from everyone who installs the services, just that it has the right to do so if it chooses. You agree to this when you install it.
Other online distribution services have similar EULAs in place, and some allow you to opt out, some do not, so in the end - it is up to you to decide how much information you want third-parties to have regarding your system.