I like adding functions to jQuery so this function would help:

jQuery.fn.center = function () {
    this.css("position","absolute");
    this.css("top", Math.max(0, (($(window).height() - $(this).outerHeight()) / 2) + 
                                                $(window).scrollTop()) + "px");
    this.css("left", Math.max(0, (($(window).width() - $(this).outerWidth()) / 2) + 
                                                $(window).scrollLeft()) + "px");
    return this;
}

Now we can just write:

$(element).center();

Demo: Fiddle (with added parameter)

I put a jquery plugin here

VERY SHORT VERSION

$('#myDiv').css({top:'50%',left:'50%',margin:'-'+($('#myDiv').height() / 2)+'px 0 0 -'+($('#myDiv').width() / 2)+'px'});

SHORT VERSION

(function($){
    $.fn.extend({
        center: function () {
            return this.each(function() {
                var top = ($(window).height() - $(this).outerHeight()) / 2;
                var left = ($(window).width() - $(this).outerWidth()) / 2;
                $(this).css({position:'absolute', margin:0, top: (top > 0 ? top : 0)+'px', left: (left > 0 ? left : 0)+'px'});
            });
        }
    }); 
})(jQuery);

Activated by this code :

$('#mainDiv').center();

PLUGIN VERSION

(function($){
     $.fn.extend({
          center: function (options) {
               var options =  $.extend({ // Default values
                    inside:window, // element, center into window
                    transition: 0, // millisecond, transition time
                    minX:0, // pixel, minimum left element value
                    minY:0, // pixel, minimum top element value
                    withScrolling:true, // booleen, take care of the scrollbar (scrollTop)
                    vertical:true, // booleen, center vertical
                    horizontal:true // booleen, center horizontal
               }, options);
               return this.each(function() {
                    var props = {position:'absolute'};
                    if (options.vertical) {
                         var top = ($(options.inside).height() - $(this).outerHeight()) / 2;
                         if (options.withScrolling) top += $(options.inside).scrollTop() || 0;
                         top = (top > options.minY ? top : options.minY);
                         $.extend(props, {top: top+'px'});
                    }
                    if (options.horizontal) {
                          var left = ($(options.inside).width() - $(this).outerWidth()) / 2;
                          if (options.withScrolling) left += $(options.inside).scrollLeft() || 0;
                          left = (left > options.minX ? left : options.minX);
                          $.extend(props, {left: left+'px'});
                    }
                    if (options.transition > 0) $(this).animate(props, options.transition);
                    else $(this).css(props);
                    return $(this);
               });
          }
     });
})(jQuery);

Activated by this code :

$(document).ready(function(){
    $('#mainDiv').center();
    $(window).bind('resize', function() {
        $('#mainDiv').center({transition:300});
    });
);

is that right ?

UPDATE :

From CSS-Tricks

.center {
  position: absolute;
  left: 50%;
  top: 50%;
  transform: translate(-50%, -50%); /* Yep! */
  width: 48%;
  height: 59%;
}

I would recommend jQueryUI Position utility

$('your-selector').position({
    of: $(window)
});

which gives you much more possibilities than only centering ...

This is untested, but something like this should work.

var myElement = $('#myElement');
myElement.css({
    position: 'absolute',
    left: '50%',
    'margin-left': 0 - (myElement.width() / 2)
});

Edit:

If the question taught me anything, it's this: don't change something that already works :)

I'm providing an (almost) verbatim copy of how this was handled on http://www.jakpsatweb.cz/css/css-vertical-center-solution.html - it's heavily hacked for IE but provides a pure CSS way of answering the question:

.container {display:table; height:100%; position:absolute; overflow:hidden; width:100%;}
.helper    {#position:absolute; #top:50%;
            display:table-cell; vertical-align:middle;}
.content   {#position:relative; #top:-50%;
            margin:0 auto; width:200px; border:1px solid orange;}

Fiddle: http://jsfiddle.net/S9upd/4/

I've run this through browsershots and it seems fine; if for nothing else, I'll keep the original below so that margin percentage handling as dictated by CSS spec sees the light of day.

Original:

Looks like I'm late to the party!

There are some comments above that suggest this is a CSS question - separation of concerns and all. Let me preface this by saying that CSS really shot itself in the foot on this one. I mean, how easy would it be to do this:

.container {
    position:absolute;
    left: 50%;
    top: 50%;
    overflow:visible;
}
.content {
    position:relative;
    margin:-50% 50% 50% -50%;
}

Right? Container's top left corner would be in the center of the screen, and with negative margins the content will magically reappear in the absolute center of the page! http://jsfiddle.net/rJPPc/

Wrong! Horizontal positioning is OK, but vertically... Oh, I see. Apparently in css, when setting top margins in %, the value is calculated as a percentage always relative to the width of the containing block. Like apples and oranges! If you don't trust me or Mozilla doco, have a play with the fiddle above by adjusting content width and be amazed.

Now, with CSS being my bread and butter, I was not about to give up. At the same time, I prefer things easy, so I've borrowed the findings of a Czech CSS guru and made it into a working fiddle. Long story short, we create a table in which vertical-align is set to middle:

<table class="super-centered"><tr><td>
    <div class="content">
        <p>I am centered like a boss!</p>
    </div>
</td></tr></table>

And than the content's position is fine-tuned with good old margin:0 auto;:

.super-centered {position:absolute; width:100%;height:100%;vertical-align:middle;}
.content {margin:0 auto;width:200px;}​

Working fiddle as promised: http://jsfiddle.net/teDQ2/

Just say: $("#divID").html($('').html($("#divID").html()));

It can be done with only CSS. But they asked with jQuery or JavaScript

Here, use CSS Flex box property to align the div center.

body.center{
  display:flex;
  align-items:center; // Vertical alignment
  justify-content:center; // Horizontal alignment
}

align-items:center; - used to align vertically.

justify-content:center; - used to align horizontally.

document.querySelector("body").classList.add("center");

body {
  margin : 0;
  height:100vh;
  width:100%;
  background: #ccc;
}
#main{
  background:#00cc00;
  width:100px;
  height:100px;
}
body.center{
  display:flex;
  align-items:center;
  justify-content:center;
}

<body>
  <div id="main"></div>
</body>

I used this to put the UL in the middle position.

cadasWidth          = $('.card-dashboard').innerWidth();
cadasWidthCenter    = cadasWidth/2;

ulmenuWidth         = $('.card-dashboard ul#menu').outerWidth();
ulmenuWidthCenter   = ulmenuWidth/2;

ulmenuStart = cadasWidthCenter - ulmenuWidthCenter;

$('.card-dashboard ul#menu').css({
    'left' : ulmenuStart,
    'position' : 'relative'
});