How can I turn off the dizzying iOS 7 motion effects? My girlfriend is getting that well-publicized nausea/dizziness/"carsickness" from iOS 7's motion effects, though I'm not sure if it's because of the wallpaper or the animations overall. What can she do to tone them down? Are there options built into the software?
Yes, she can change the behavior.

From Apple's page on "iOS 7: How to reduce screen motion":


  Learn how to reduce screen motion in iOS 7.
  
  iOS 7 uses a parallax effect to create the perception of depth on your Home screen and elsewhere. When this feature is on, you may notice that your:
  
  Wallpaper, icons, and alerts shift slightly as you move your phone.
  When setting a wallpaper in Settings > Wallpapers &amp; Brightness, the photo or image will be slightly zoomed and cannot be scaled to fit to the screen.
  
  You can change this behavior by enabling Settings > General > Accessibility > Reduce Motion.
  
  Note: If zoomed, you will need to rescale your wallpaper to fit to the screen.
  
  Additional Information
  
  To learn more about iOS 7, refer to the user manual.




Also see "What are some hidden or undocumented features in iOS 7?" here.