Assuming the link text is colored, it's not always absolutely necessary to underline it.
* There are two main cases in which you can safely eliminate underlines: navigation menus and other lists of links. However, this is true only when the page design clearly indicates the area's function. (Remember: your design might not be as obvious to outside users as it is to your own team members.) Users typically understand a left-hand navigation rail with a list of links on a colored background, assuming it resembles the navigation areas on most other sites.
* Exception: underlining is essential if you use link colors such as reds or greens, which cause problems for users with common forms of color-blindness.
* Exception: underlined links are important for low-vision users' accessibility, so retain underlines if accessibility is a priority for your site or you have many users with low vision.