There's a dedicated "Privacy" setting in the Settings app. You could disable everything from there, including some Location Services, even the ones used for system services like Cell Network Search and setting the time zone.

Additionally, you can turn off Siri completely under Siri settings. You can also turn off Siri and Bing/Spotlight suggestions under Spotlight settings. iCloud could also be turned off.

That said, by turning the above features off, why are you using a smartphone in the first place?

Apple has been making great strides in user privacy lately, and I think they genuinely care about our privacy, what with them encrypting everything and not having the keys to decrypt it themselves (so they say).

I choose to trust my privacy with Apple. They've given me no reason to doubt them, yet.