I happen to have an iPhone and I'm constantly stumbling across things that I didn't know it could do.  I've picked up a few hints and tricks here and there, but this article from Buzzfeed completely blew my mind.  Here's a few of the tricks I think I'll be using the most.

Siri Will Read You Your E-mail

This is super helpful when I'm on the go.  Tell Siri to "Read my e-mail" and he/she will give you sender's name, when the message was received and the subject.  She can also tell you to read your last e-mail and ask if you have a message from a certain sender.

Show You Several Days Of Your Agenda At A Time

If you turn your phone sideways when the calendar app is open you'll see more days/details of your agenda.  Just make sure your portrait orientation lock is turned OFF when you try this.