<a href="https://silentcircle.com/web/how-it-works/" target="_blank">Silent Circle's "Silent Suite"</a> for iPhone and Android encrypts phone calls, files, texts, emails and video recordings, and can be set to erase them all from a sender's device within minutes of sending. When the app hit the market in October of last year, Slate said the product "<a href="http://www.slate.com/articles/technology/future_tense/2012/10/silent_circle_mike_janke_s_iphone_app_makes_encryption_easy_governments.single.html" target="_blank">has governments nervous</a>."
Redphone & TextSecure
If Silent Circle's $120 annual subscription fee is too much, but you still want the option of encrypting your calls and texts, try <a href="https://whispersystems.org/" target="_blank">Open WhisperSystems' free security apps</a> for iPhone and Android. Redphone allows users to encrypt their phone calls, while TextSecure allows them to do the same for texts.
Orbot & Onion Browser
The Android app <a href="https://play.google.com/store/apps/details?id=org.torproject.android&feature=search_result#?t=W251bGwsMSwxLDEsIm9yZy50b3Jwcm9qZWN0LmFuZHJvaWQiXQ" target="_blank">Orbot</a> lets you browse the web anonymously on your phone and would seemingly prevent <a href="http://www.huffingtonpost.com/2012/07/09/app-privacy-ads_n_1658191.html" target="_blank">advertising networks or others from getting information</a> about you based on your mobile web browsings. The <a href="https://itunes.apple.com/us/app/onion-browser/id519296448?mt=8" target="_blank">Onion Browser</a> works similarly, but for the iPhone.
Cloudfogger & NoteCipher
If you're afraid of storing information in the Cloud, you can try <a href="https://play.google.com/store/apps/details?id=com.cloudfogger.cf&hl=en" target="_blank">Cloudfogger</a>, an open-source Android and iPhone app that encrypts anything you store in the Cloud. If you have an Android phone, you can also pair that with <a href="https://play.google.com/store/apps/details?id=info.guardianproject.notepadbot" target="_blank">the Guardian Project's NoteCipher</a>, which encrypts notes on your phone's hard drive.
<a href="https://play.google.com/store/apps/details?id=com.duckduckgo.mobile.android&hl=en" target="_blank">A search engine called DuckDuckGo</a>, available for the Android and the iPhone, has built its reputation around privacy. It doesn't track or store searches, and people who use it are effectively anonymous.
Gemini App Manager
Smartphone users can generally uninstall (or avoid altogether) apps that they believe compromise their privacy -- unless those apps are "<a href="http://whatisbloatware.com/" target="_blank">bloatware</a>," apps pre-installed by the phone's carrier and impossible to remove by normal means. The <a href="https://play.google.com/store/apps/details?id=com.seasmind.android.gmappmgr&feature=search_result#?t=W251bGwsMSwxLDEsImNvbS5zZWFzbWluZC5hbmRyb2lkLmdtYXBwbWdyIl0" target="_blank">Gemini App Manager</a> for Android allows <a href="http://www.howtogeek.com/115533/how-to-disable-or-uninstall-android-bloatware/" target="_blank">users to get around the phone's restrictions and disable the bloatware</a>, thus removing potentially privacy-invading apps.
The <a href="https://play.google.com/store/apps/details?id=org.safermobile.intheclear" target="_blank">InTheClear</a> app allows you to delete all your personal data on your Android phone in an instant by pressing the app's red "Panic!" button. You can also use the app to send an emergency text message when the Panic! button is pressed, so that your compatriots know that you've wiped your cell and might be in serious trouble.