jQuery plugin authoring: Vertical Center example
Interesting question, from a once over:


Consider a 'use strict' after (function( $ ){
You are mixing lowerCamelCase and snake_case, you should stick to lowerCamelCase
I am not a fan of remove_style, it might cause all kinds of unintended consequences, it would be better to store the original values of element and parent and then restore them if we don't center.
I am also not a fan of having 1 listener function per element ( however, if you were to keep the original css info in a closure, then that's fine )
The code would probably be cleaner if you let center_element determine the parent.
The newlines before closing curly braces make the code a bit too sparse towards the end


I would probably try something like this:

(function($){
  'use strict';
  $.fn.verticalCenter = function(options) {

    var settings = $.extend({
      min: 0,    // Minimum width of the viewport for centering to take effect
      max: 10000 // Maximum width of the viewport
    }, options);

    var centerElement = function(element,parent){

      parent.css({ position:'relative' });
      element.css({
        position: 'absolute',
        top: "50%",
        marginTop:-element.height() / 2
      });
    };

    var determine_action = function(element){

      var parent = element.parent(),
          originalParentStyle = parent.style(['position']),
          originalElementStyle = element.style(['position','top','marginTop']);

      $(window).on('load resize orientationchange', function() {

        var windowWidth = window.innerWidth;

        if (windowWidth &gt; settings.min &amp;&amp; windowWidth &lt; settings.max) {
          centerElement(element, parent);
        }
        else {
          parent.css(originalParentStyle);
          element.css(originalElementStyle);
        }
      });
    };

    return this.each(function(){
      determine_action($(this));
    });
  };
})(jQuery);