It is amazing to me how this suggestion causes so much angst and fighting. Designers often argue that they look ugly, some users claim they are distracting, others even claim they reduce accessibility.
I’ve tried to gather some information here to allow you to make your own judgment, which may or may not end up matching mine. If you understand the resources I provide and still do not agree, that is fine. However, if you understand the resources I provide then I suspect you will at least style links in a way that makes them usable.Remember, this is for addressing how links are styled in the body of a page, the narrative content, where they sit among blocks of unlinked text. Not navigation, not footers, not page controls, etc.
Fair warning, this is a lengthy post. I’ve broken it into six sections: