One feature/change per post. Please search the current answers before listing yours. If it's difficult to explain with words, please use pictures. Changes that can increase productivity of the user, consumption of media are likely to attract more votes. The change could have been made in any current revision of iOS7, but has to still be available in iOS7.0.3.
My favorite new feature is the ability to 'reduce motion' via Settings > Accessibility > Reduce Motion.
When enabled, the animation for launching an app and going to the home screen are greatly reduced, which allows me to access the phone from its locked state more quickly, and is more valuable to me than having zooming animations.