I think you have to weigh several factors.
One is the design of the site. With some things, the links are obvious even without underlines. Examples would be navigation menus. You don't need menu items to be underlined for people to realize they need to click on it.
I have seen some sites use bold
rather than underlines
[webmasterworld.com] for links. Sometimes, that makes the links stand out even better than an underline, especially in paragraphs of text. The bold text pops out while underlined text may sometimes blend in.
And, depending on your site colors, leaving the links the standard colors may look bad.
You also want to consider what type of visitor you have. Do you have a site where people come in, find a link, click it and leave? If so, you might stick with standard link conventions so the links can be easy to spot so that they can get in and out of your site to their destination.
On the other hand, if your site is meant to be one people will visit again and again, then you have a bit more flexibility with your linking designs. If they will be spending a lot of time on your site, they will learn your site's conventions.