How do you disable system apps in Android 4.x.x (and up)? I heard you can "freeze" or "disable" system apps starting in Android 4.0 without rooting. How do you do it?
You can disable only System apps from Android 4.0 onwards.

Check the guide here with video.

Basically you have to:


  
  Go to your phone’s main settings menu.
  Go to the “Apps” or “Applications” option.
  Go to the “All” tab in your list of apps.
  Find the app you wish to disable and tap on it.
  Press the disable button next to the force stop button.
  If the disable button isn’t
  visible, you have to press “uninstall updates” first. Then go back
  to step 5
  


To enable it again: 


  Once you’ve disabled the app, it will be hidden from your phone as if
  it were never there. The great news is if you ever wanted it back, all
  you have to do is the same process but “enable” it instead. Just to
  let you know, disabled apps show up at the very bottom of the app list
  (not in alphabetical order) if you ever wish to re-enable it.


Update:

To disable user installed apps I use this aswesome software called Titanium backup pro (needs root). Freezing app i.e. disabling app is only one of its many features.

To freeze one app:


Open Titanium backup pro  
Go to Backup and Restore tab
Find you app and click it
Choose freeze from the menu
To restore click defrost instead of freeze


Note: Freezing app still consumes space.

I personally use this to freeze heavy app like Skype. Application settings like username and password aren't lost in this way.