I am new to Unity 4.6.x and I would like a simple to implement transition solution (fade between, fade to black, pixelate, etc.) that I can leverage when I call Application.LoadLevel. It needs to work on iOS, OS X, Windows, Windows Phone 8.x and Android.

You can just change the alpha value on a black fullscreen panel/image to fade to black. Once the alpha reaches 1, switch levels. Then in the next level, start with a fullscreen black panel/image and get rid of it by changing the alpha value again.