Edit in JSFiddle

document.getElementById("mouse-events").addEventListener("mouseenter", function () {
    this.style.background = "#f00";
}, false);

document.getElementById("mouse-events").addEventListener("mouseleave", function () {
    this.style.background = "#fff";
}, false);

<div id="mouse-events">Hello, dear <a href="http://hacks.mozilla.org/">Mozila Hacks readers</a> struggled with mouse events</div>

#mouse-events {
    padding: 20px;
}