1. Lock your phone and use a strong password
2. Use 'Find My iPhone' or a similar service
Not only does this protect your data, it could help you recover your phone.
3. Don't leave your smartphone unattended or lend it to a stranger
Don't leave your phone out in public where it can be grabbed by an opportunist.
The person who needs to make an emergency call could be in legitimate need of help--or not. Make the call yourself, and put it on speakerphone. Do not hand the person your phone.
4. Update your smartphone
Smartphone system updates may include security updates.
5. Manage location settings
Most phones come with location tracking features. This is good when you are using a map. Many apps come with location tracking. You can turn this off in most cases. If you want to make your location as secret as possible, turn off all forms of location tracking.
6. Download apps only from official apps stores
Apps that have not been approved by an official app store are more likely to be invasive.
7. Find out everything an app does before installing it
Read the "Permissions" screen. What data is being accessed/stored:
Where and how long will it be stored? Will it be sent to 3rd parties? What do the app reviews say?
8. Beware of attachments and links in email
If in doubt about a site, check it here:
9. Encrypt Smartphone Data
How to encrypt your smartphone for iOS and Android
10. Run anti-virus software: