p { color: navy; }

.a a:hover { background: green; color: white; }

.b a:hover { background: red; color: yellow; }
.b a:link { background: green; color: white; }

.c :link { background: green; color: white; }
.c :visited:hover { background: red; color: yellow; }

<p class="a">The background color of <a href="#foo">this anchor (<strong>here</strong>)</a> should turn to green when the pointing device hovers over it.</p>
<p class="b">The background color of <a href="#foo">this anchor (<strong>here</strong>)</a> should <strong>remain green when you hover it</strong>.</p>
<p class="c">The background color of <a href="http://link.example.com/">this anchor (<strong>here</strong>)</a> should <strong>remain green when the pointing device hovers over it</strong> (do not follow that link).</p>