Your phone is just a computer. It's got a browser, operating system, location tracker and apps that want your data. It might just be the best snooping device ever invented, but you can take steps to reduce risks and increase your security.
DuckDuckGo's SpreadPrivacy.com has great resources for mobile privacy tips for iPhone, Windows, and Android
You might be surprised that some of the most popular apps don't have the best privacy features, take a look with Privacy Check.
Thinking of a new messenger app that emphasizes privacy? Look at this comparison chart for some new alternatives.
2 Factor Authentication is a complete 'must have' these days, so set it up on your phone for all accounts that support that. Check which sites and apps offer it.
For online searching and browsing, use DuckDuckGo or Firefox Focus and look into DNS for Mobile for a speed increase and privacy boost.
For those that really need top notch security, Orfox and TOR for Android are options.
Some other helpful mobile security tips