IPhone – My iPhone 5s is cracked and the screen is black, how to get pictures from the phone

The rotation lock may have been turned on.

To change this:

1. Double-tap the home button to show the app switcher at the bottom.
2. Swipe to the right, and you'll see the music controls and the rotation lock switch (the icon at the far left). If rotation is locked, there will be a lock symbol inside the arrow circle.
3. Tap the rotation switch to unlock it. (The text: 'Portrait Orientation Unlocked' will appear at the bottom).

This has changed with recent (2015) updates. On the home screen slide your thumb from the bottom up to get to the quick settings. On the top right you should see the rotation lock. Tap it and rotate should work again.

I think your best bet is to to run your iphone side by side with another iphone that is also set to lock. Now, by using the two phones side by side, you should be able to enter your passcode 'blind' using the position of the keys on the working phone as a guide.