Many people use their smartphones as it comes, bone stock. If you're on Android, you really should check the great Android security functions you could be using.
Disable App Notification Permissions
If there's an app that constantly pushes notifications and you still wish to use said app, you can disable the notification permission from the app. Simply go to Settings > Apps > and then tap the offending app. Finally, uncheck Show notifications.
Disable Unwanted Preinstalled Apps
You still can't remove preinstalled apps completely but you can disable them. I had to disable 8 bloatware apps on my Galaxy S4. If you wish to disable your annoying apps, simply go to Settings > Apps > Select the All category and then tap the app you wish to disable. The disable button is where the uninstall button would normally be.
Encrypt Your Device
Simply go to Settings > Security > and tap Encrypt phone or tablet, depending on which device you are using.
Note: This encryption process will encrypt the entire storage, which will take quite a bit of time. A password will be required every time you power on the device. If you forget this password you can still get into your device through a factory reset. This will wipe all of your data.
Restrict App Background Cellular Data Access
With extremely low data caps it is imperative to deter apps while you are not connected to Wifi. What you are actually doing is restricting the app's data connection in the background. Simply go to Settings > Data usage. Select an app that uses data and check Restrict mobile data.
Note: If you open the app, the app can still use data on a Wifi network. However, the app will not use data through the cellular data connection in the background.
Note 2: If you select Mobile hotspots under your menu, you can specify a Wifi network that should be treated as a mobile network. This Wifi network will be treated in the same manner as the cellular data network.
VPN access isn't a necessity per se, but it is a nifty native feature you can use without installing other apps or even rooting your device. Simply go to Settings > Under Wireless & Networks tap More > VPN.
Note: Multiple VPN profiles are possible.
So what other Android security functions do you look at? Let me know.
Update: When you're ready to sell your Android phone, check out this mobile migration checklist.