I just don't use any services. I can and have deleted/disabled maps/location from the phone. I prefer printed driving directions so that's no big loss. I only use Gmail accounts for oddball stuff and Play. I use another email service not allied to a portal like Google, Yahoo, etc. GMail on phone is disabled. I bought Aquamail. K9 is another good app.
If you want a photo editor, there's plenty. You don't have to use Picasa. I use Aviary. I have a Flickr account, but end up sending a lot of stuff by Dropbox. There are other image posting apps. I don't keep You can usually turn off location in camera app.
Color Notes does have a calendar. It isn't too easy to sync., but it does work for appointments. I don't need an Office app, but if I did, I have a sideways upgrade to Documents to Go. (Had it on Palm.) There are others.
MX video player is good. I bought it on the tablet. I had to find an audio app that dealt with MID files. I use those for ringtones.
READ THE PERMISSIONS and TOS before installing or updating. If Play isn't giving you enough info, try looking up the app on AppBrain.
If you must use Twitter or FB, disable them between uses. You can disable G+.
Turn off Google location service. The carrier's you can't. Turn off GPS if you don't use it. I leave it on for astronomy and weather.
There's other map services if you want a map. Some are mentioned here for offline use.
I don't want that search icon on the desktop, a good launcher hides it. I've gone to Google Dashboard and deleted any info there. It still shows I have a Blogger account, but there's nothing in it. I gave up Google voice number. Never used it. I have everything set to no notification. Apps are set to not automatically update.
I don't do any shopping, or download movies or music on the phone. I usually use my computer which has Ghostery and NoScript plus a few other extensions for privacy. I do use data to look up information. I'll follow baseball scores.
I also get a browser which supports other search engines. Dolphin is secure and it supports Duck, Duck Go as a default.
I've added a couple of others.
The Firefox browser for Android does use Ghostery and one other privacy extension. I just can't stand the UI.
I have nothing personal on the phone except text messages and phone book which is not synced to Google.
I figured out how to use VCF files. I also use a GSM phone which will sync with a SIM card. I do keep track of spending, but there are no account names or numbers.
I've turned off NFC, and usually have Bluetooth turned off. I don't like earpieces and forget to charge them.
I use an Android for the great nature and astronomy reference apps. I can't put those on a dumb phone. They are all paid apps to boot. I don't mind paying for a good app.
The privacy issue is more about where I live. Most of the stuff you get bombarded with is local. I had enough years ago with constant phone spam from businesses, so I will buy as little as possible from local merchants. I'll drive to another town that has what I want. I also let my fingers do the walking. I had one rule with landline spam. If you pester me, I don't do business with you.
I don't buy the carrier's phones. TMOUS is pretty good about bring your own device. Right now, I have the Oppo Find 7 which has the TMO bands. I bought one carrier smart phone and had an app that kept turning itself on and searching. It could do nothing as I wouldn't sign up, but it did waste battery. That phone, a Samsung, got rooted. I've rooted a Nexus S and a Nexus 4. So far, the Oppo hasn't bothered me with extra junk, so I haven't rooted it.