Why it's good to use underlining for links?

There are different design tricks to make links different from surrounding text. The most traditional way to increase clickablity is to use underlined text style. Often web designers hesitate to use underlining because it looks too traditional, even boring. That is true, that it was the way links were designated 15-20 years ago, but you should also keep in mind, that users habits are formed during the time and they change slowly.

It is surely possible to experiment with not underlining links and use only color instead. However, it is important not to use link style for other parts in text, which are not clickable.

For example, if you decide to underline links in your website, don't use underlining for other texts. In this way you ensure, that links are clearly different form any other page element.

Same style across the site
It is suggested to use same style as consistently as possible across entire website. It means, that if you decided to underline links, do it in every section and subpage. It quarantees, that users percieve they are links and click them more often.  

What about navigation menus?
Not all links are same in the website. Making links stand out from surrounding text is most important in the content, where you have large chunks of texts and some links inside of them.

Links in navigation menu are percieved more as links because of placement and context. In most of times, there are only links in navigation menu, so you don't have really problem of making difference between non-links and links there. Just make sure, that navigation menu is positioned and designed in a way it's function is clear.