Bordered elements with non-bordered pseudo-elements

The pseudo-elements indeed don't have any borders, which means setting border-bottom: 0 does nothing; however, as they are part of the originating li elements, they are rendered within the li element boxes and so the li borders extend to the pseudo-elements.

A simple solution to this problem is to apply the border to the a child elements instead of the li elements. This way the pseudo-elements exist separately from the bordered boxes.

If you need the last item to have a border as well, you could wrap its text in a span element and apply the border to li > a, li > span:

<ul class="horizontal-list">
    <li><a href="/home.html">Here's a link</a></li>
    <li><a href="/home/subpage.html">Here's another link</a></li>
    <li><span>Here's the final link</span></li>
</ul>

... but if you prefer to do this in pure CSS without the use of extraneous markup, you will need to

1. change the :before pseudo-elements to :after pseudo-elements,
2. apply the pseudo-elements to all but the last li (li:not(:last-child)) instead of all but the first (li + li), and
3. apply the border to the a elements as well as the last li.

Keep in mind that the use of :last-child will cost you IE8 compatibility; if that is a priority then you will have to make do with using a span element with li + li:before as mentioned above.

ul.horizontal-list > li:not(:last-child):after {
    content: ">";
    padding: 0 3px;
}

ul.horizontal-list > li > a, ul.horizontal-list > li:last-child {
    text-decoration: none;
    border-bottom: 1px solid #000;
}

Updated fiddle

On a final note, since all of the boxes (including the pseudo-elements) are inline, using whitespace instead of padding will provide consistent spacing between the pseudo-elements and the rest of the text:

ul.horizontal-list > li:not(:last-child):after {
    content: " > ";
}

(Technically, you don't need the trailing space because the newline after each </li> end tag fulfills the role of whitespace for this purpose, but you can include it for the sake of consistency and it will collapse normally.)