On activation of a Google account on your device, you will be asked whether you want to backup your data to the Google cloud. While this must be explicitly supported by the apps to take effect for their data (which only a few do), and thus will never be a complete data backup, many of your most private data will be affected here – amongst others your WiFi APs including their (plain text!) passwords, which even might lead to other issues beside privacy. But even if you answer this with "No", your contacts, calendars, and more will be automatically sync'd with the Google cloud without you being explicitly asked for.
So here are some things you might want to consider. The list is definitly not complete, I certainly have missed some points (and might add some lateron).
- "Do you want to backup …" (see above): This includes data of some apps which support it, a list of apps installed on the device – but also sensitive data such as configured WiFi APs with their passwords in plain-text (open issue #57560)
- In the sync settings of your Google account, de-select what you don't want to sync. Do this before entering any of your private data (contacts, calendars, etc.), and remember you will have to re-do this after a factory-reset. Side-effect: the less you sync, the less this can eat your data-plan.
- Consider switching the default storage in your contacts/calendar/... app from "Google Account" to "Device"1
- Android 4.4+: Install an alternative SMS app and make it the default one (in Settings→WiFi you can chose which app to be used for SMS) to avoid your messages being mixed into Hangouts. To be on the safe side, you can also disable SMS support in Hangouts.
- Android 4.4+: Install an alternative Gallery app2 to avoid your images being mixed with Google+ (looks like the separate gallery app will be gone soon as well). Side-effect: again savings on your data-plan for not automatically syncing all your photos (alternatively, photo sync/instant upload can also be turned off in G+ settings AFAIK).
- Avoid services like Google+ which are quite intrusive to privacy. If that's not an option for you, check their settings thoroughly, and opt-out from intrusives whereever possible.
- Disable Google Maps and replace it by a good alternative. Apps like the open-source OsmAnd, OruxMaps, or Locus Map not only offer you much better offline capabilities, but also save your device's juice by not constantly running in the background even without being explicitly started by you.
- If you followed all above suggestions, you now might as well think about disabling Google Now – it no longer can tell you it's "10 minutes to your parents", or "you need to start to work earlier because of higher traffic", as it doesn't know where (or who) your parents are, and where your work place is (or what the traffic conditions are). And cannot give you advices like "buying this because your friends like it".
- Just discovered: Google Settings › Smart Lock for Passwords. Enabled by default, it saves passwords of your apps and websites to Google's cloud (your account). Not sure if it honors the initial "Do you want to backup …" setting.
There are several more things you can do for your privacy, not being restricted to Google's services. If rooting is an option for you, things like Xprivacy are definitly worth a look. A good starting point are our privacy tag-wiki and other questions tagged "privacy".
PS: Turning WiFi off when you don't need it (with 4.3+, remember there's also the "keep scanning for networks even if WiFi is switched off" setting in Settings→WiFi→Advanced to be considered) could even protect you against being tracked by advertising trashcans...
1 There are alternative sync possibilities like OwnCloud, Funambol, and others available
2 QuickPic is a good candidate here