Securing your phone is a very important thing in this day and age. If you get mugged, if you get a virus, or get pulled over by a cop that wants to peak in your phone. Securing your info is essential to keeping your information private and out of others sights.
To help protect your information you can encrypt your hard data drive by using the default encryption program on the device. Though this program is known to cause some problems when you are rooted and needing to reset information. I personally don't care for everything to be encrypted just the important stuff.
I personally use Cryptonite to create an encrypted folder kinda of like that or truecrypt. This can then easily be pared with dropbox or ubuntuone to keep a backup of it for you. This will keep your info away from the eyes of those that want to steal it. Though the only real way to protect your phone calls and sms is by doing a full encryption.
If your phone does get stolen the best way to protect your information is to get your phone back. I use Avast anti virus and anti Theft for this process. Avast has many neat tools that we have mentioned before. Avast anti theft with root will create a partition to keep it on there so if anyone tries to reflash the phone or throw a new SIM in the phone you will be alerted with the phone number and the hardware ID. This app also comes with privacy identify and firewall to help protect your information by preventing which apps have internet access.
If you want to also protect against your carrier or the government from snooping on your emails. you can encrypt your emails by using APG and K9 together to send pgp encrypted emails to your contacts or work. This will help keep those government off your trail when trying to send top secret business information between you and your customer. You can never take encryption to seriously when there is the likes of china that try to steal business secrets from companies and that support hacking companies. If your emails are encrypted it helps prevent that.
Removing permissions from apps is probably the hardest thing. This can break many apps and it is a lot easier just denying the app internet connection than braking the app. Though you can use apps like Lucky Patcher or Permission Denied. I personally use the Lucky Patcher as it is free and helps make modified APKs that I can backup and install on non rooted devices.
Using the Tor network will help keep your information private from the government and also from your carrier. There are tools like Orbot that will change all data connections through a proxy or if your have root can set up select applications like only your web browser to use the tor network so when you want to watch youtube you don't have to wait a long time to have it load.
These are only a few of the things that you can do. There are others things like using a pin to start your device, turning off usb adb interface, keeping android updated, and using strong passwords. Don't expect the carriers to keep you updated on security patches and take your security in your own hands.
-Local Tech Repair Admin
btw I am not responsible to you lossing data or breaking your phone for doing anything stupid based on this advice.