FACC: Android comes Free of charge, is Ad supported, Cloud based, and highly Customizable
Google says it logs your "phone number, calling-party number, forwarding numbers, time and date of calls, duration of calls, SMS routing information and types of calls" in their privacy policy. It also logs your IP address.

"We may collect device-specific information (such as your hardware model, operating system version, unique device identifiers, and mobile network information including phone number). Google may associate your device identifiers or phone number with your Google Account."
While Android itself is Open Source, many apps are not.
http://android.stackexchange.com/questions/43361/what-information-does-stock-android-send-to-google-by-default-and-how-do-i-opt

Staying in the current system
-> alternative to google play, with only free software apps
the Apk Android application package file Freedroid
F-Droid is an installable catalogue of FOSS (Free and Open Source Software) applications for the Android platform. 
This is what the Fsfe supports
https://f-droid.org/

-> if you want to hide, encrypt your communication
https://guardianproject.info/
Their terminology:
Apps And Tools You Can Trust 
notice the emphasis on trust
https://guardianproject.info/apps/

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Back-up :-)

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Why root?
What is root?

Android, despite being open source, still did not give a user complete control over the device. This laid basis for many potential abilities remaining dormant, and subsequently Android devices began to get ‘rooted’. Now this begets the question, why root? With so many Android-based handsets out there now, this question has become even more important.

Rooting essentially means gaining root-level access to your device. Rooting means you are the master and in control, not to mention the fun of it.

Phone dependant


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Change the OS - Phone dependant

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Most free: http://replicant.us/
Only for specific phones..
http://replicant.us/supported-phones/

Other OS's
https://en.wikipedia.org/wiki/Comparison_of_mobile_operating_systems
- Firefox
- Cyanogenmod
A stripped non-free ROM is still a non-free ROM
https://public.pad.fsfe.org/p/MarvinsAndroidIdea
- Ubuntu Touch for the future


Future G**gle plans
===============
It seems certain that Android ROMs without Google Apps are going to get harder
to make as core functionality is increasingly being moved out of the core OS
and into proprietary Google packages.
http://arstechnica.com/gadgets/2013/09/balky-carriers-and-slow-oems-step-aside-google-is-defragging-android/