Center icon in a div - horizontally and vertically

Since they are already inline-block child elements, you can set text-align:center on the parent without having to set a width or margin:0px auto on the child. Meaning it will work for dynamically generated content with varying widths.

.img_container, .img_container2 {
    text-align: center;
}

This will center the child within both div containers.

UPDATE:

For vertical centering, you can use the calc() function assuming the height of the icon is known.

.img_container > i, .img_container2 > i {
    position:relative;
    top: calc(50% - 10px); /* 50% - 3/4 of icon height */
}

jsFiddle demo - it works.

For what it's worth - you can also use vertical-align:middle assuming display:table-cell is set on the parent.

Here is a way to center content both vertically and horizontally in any situation, which is useful when you do not know the width or height or both:

CSS

#container {
    display: table;
    width: 300px; /* not required, just for example */
    height: 400px; /* not required, just for example */
}

#update {
    display: table-cell;
    vertical-align: middle;
    text-align: center;
}

HTML

<div id="container">
    <a id="update" href="#">
        <i class="icon-refresh"></i>
    </a>
</div>

JSFiddle

Note that the width and height values are just for demonstration here, you can change them to anything you want (or remove them entirely) and it will still work because the vertical centering here is a product of the way the table-cell display property works.