Custom li list-style with font-awesome icon

The CSS Lists and Counters Module Level 3 introduces the ::marker pseudo-element. From what I've understood it would allow such a thing. Unfortunately, no browser seems to support it.

What you can do is add some padding to the parent ul and pull the icon into that padding:

ul {
  list-style: none;
  padding: 0;
}
li {
  padding-left: 1.3em;
}
li:before {
  content: "\f00c"; /* FontAwesome Unicode */
  font-family: FontAwesome;
  display: inline-block;
  margin-left: -1.3em; /* same as padding-left set on li */
  width: 1.3em; /* same as padding-left set on li */
}

<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/font-awesome/4.5.0/css/font-awesome.min.css">
<ul>
  <li>Item one</li>
  <li>Item two</li>
</ul>

Adjust the padding/font-size/etc to your liking, and that's it.

You could and should also put the spacing unit in a css variable instead of repeating it throughout the code.

=====

This works with any type of iconic font. FontAwesome, however, provides their own way to deal with this 'problem'. Check out Darrrrrren's answer below for more details.

As per the Font Awesome Documentation:

<ul class="fa-ul">
  <li><i class="fa-li fa fa-check"></i>Barbabella</li>
  <li><i class="fa-li fa fa-check"></i>Barbaletta</li>
  <li><i class="fa-li fa fa-check"></i>Barbalala</li>
</ul>

Or, using Jade:

ul.fa-ul
  li
    i.fa-li.fa.fa-check
    | Barbabella
  li
    i.fa-li.fa.fa-check
    | Barbaletta
  li
    i.fa-li.fa.fa-check
    | Barbalala

I'd like to provide an alternate, easier solution that is specific to FontAwesome. If you're using a different iconic font, JOPLOmacedo's answer is still perfectly fine for use.

FontAwesome now handles list styles internally with CSS classes.

Here's the official example:

<ul class="fa-ul">
  <li><span class="fa-li"><i class="fas fa-check-square"></i></span>List icons can</li>
  <li><span class="fa-li"><i class="fas fa-check-square"></i></span>be used to</li>
  <li><span class="fa-li"><i class="fas fa-spinner fa-pulse"></i></span>replace bullets</li>
  <li><span class="fa-li"><i class="far fa-square"></i></span>in lists</li>
</ul>