我有两个主要建议，第一：不要使用内联事件处理程序（将行为放在一个地方更易于维护），第二个是在父center_links元素上使用onmouseout。
为此目的：

function setSideText(setting) {
    if (setting == 0) // Home
    {
        document.getElementById('center_text').innerHTML = '<p><div class="dropcap">#</div>I am an information technology student interested in free and open source software.</p>';
    }
    else if (setting == 1) // About
    {
        document.getElementById('center_text').innerHTML = '<p><div class="dropcap">#</div>My name is David Gay, and this is my website. Welcome.</p>';
    }
    else if (setting == 2) // Blog
    {
        document.getElementById('center_text').innerHTML = '<p><div class="dropcap">#</div>My blog runs on the <a href="http://chyrp.net/">Chyrp</a> blog software.';
    }
}

var linksElem = document.getElementById('center_links'),
    links = linksElem.getElementsByTagName('a');

for (var i = 0, len = links.length; i < len; i++) {
    links[i].dataIndex = i+1;
    links[i].onmouseover = function() {
        setSideText(this.dataIndex);
    };
}

linksElem.onmouseout = function(){
    setSideText(0);
}

JS Fiddle demo.

• • 编辑**修改setSideText()函数，使其响应单词而不是索引（因为我认为在以后添加后续链接更容易，并且不依赖于能够向元素添加任意属性，尽管它 * 确实 * 要求元素具有id属性...）：

function setSideText(setting) {
    if (setting == 'home' || setting == 0)
    {
        document.getElementById('center_text').innerHTML = '<p><div class="dropcap">#</div>I am an information technology student interested in free and open source software.</p>';
    }
    else if (setting == 'about')
    {
        document.getElementById('center_text').innerHTML = '<p><div class="dropcap">#</div>My name is David Gay, and this is my website. Welcome.</p>';
    }
    else if (setting == 'blog')
    {
        document.getElementById('center_text').innerHTML = '<p><div class="dropcap">#</div>My blog runs on the <a href="http://chyrp.net/">Chyrp</a> blog software.';
    }
}

var linksElem = document.getElementById('center_links'),
    links = linksElem.getElementsByTagName('a');

for (var i = 0, len = links.length; i < len; i++) {
    links[i].onmouseover = function() {
        setSideText(this.id);
    };
}

linksElem.onmouseout = function(){
    setSideText(0);
}

JS Fiddle demo.

这不起作用的唯一原因是在Javascript中设置这些DOM事件时，没有大写;只需将.onMouseOut更改为.onmouseout即可。
我不知道他们为什么决定让这些事件的HTML和Javascript名称不一致（我想这是人们讨厌DOM的另一个原因）。

触发onMouseOut函数的方式与触发onMouseOver函数的方式相同
您的链接HTML需要看起来像这样：

<a href="blog" onMouseOver="javascript:setSideText(2)" onMouseOut="javascript:setSideText(0)">blog</a>

我建议研究一下jQuery--它使处理事件和DOM操作更加直接！
这里有很棒的免费课程：http://tutsplus.com/course/30-days-to-learn-jquery/