The link without an underline was done by embedding this code:
<A STYLE="text-decoration:none" HREF="link.html">This is an unusual link, it has no underline</A>
Historically, people have grown customized to underlined links. This means that users automatically associate underlined-text with links. If they see a link that isn't underlined, they might not know that it is a link.
For those reasons, before removing the underlines, there are few things to consider. First, is it a good idea to remove the underlines? Can user find links if they are not underlined? Second, consider what actual benefit would be gained by removing the underlines. It may be cool, but many user prefer to have ease of use instead.