Javascript - remove an array item by value

If you're going to be using this often (and on multiple arrays), extend the Array object to create an unset function.

Array.prototype.unset = function(value) {
    if(this.indexOf(value) != -1) { // Make sure the value exists
        this.splice(this.indexOf(value), 1);
    }   
}

tag_story.unset(56)

I like to use filter:

var id_tag = [1,2,3,78,5,6,7,8,47,34,90];

// delete where id_tag = 90
id_tag = id_tag.filter(function(x) {
    if (x !== 90) {
      return x;
    }
});

You'll want to use JavaScript's Array splice method:

var tag_story = [1,3,56,6,8,90],
    id_tag = 90,
    position = tag_story.indexOf(id_tag);

if ( ~position ) tag_story.splice(position, 1);

P.S. For an explanation of that cool ~ tilde shortcut, see this post:

Using a ~ tilde with indexOf to check for the existence of an item in an array.

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Note: IE < 9 does not support .indexOf() on arrays. If you want to make sure your code works in IE, you should use jQuery's $.inArray():

var tag_story = [1,3,56,6,8,90],
    id_tag = 90,
    position = $.inArray(id_tag, tag_story);

if ( ~position ) tag_story.splice(position, 1);

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If you want to support IE < 9 but don't already have jQuery on the page, there's no need to use it just for $.inArray. You can use this polyfill instead.

tag_story.splice(tag_story.indexOf(id_tag), 1);