An unfortunate side-effect of removing underlines from links on a web page is that one can easily miss side-by-side links. Here's an example from a blog I was reading today:
How many links are there in that section? One? Two? Three? The answer is three, but just like with this image, you can't tell by looking at it. There's a different meaning to multiple, concurrent links in a sentence like this. Someone might argue that if you care about the links, you'll go and visit each one anyway, so the end is the same. The problem is that links don't always take use places, they also give us the possibility of another place without leaving our current position; the link out of the document has meaning within the document.
The effect of multiple, concurrent links is to add semantic weight to your point via a visual cue. It overflows the sentence with examples without you having to go to them in order to get the point. However, when the underline is removed, you are led to believe that there is only one link, and unless you check, that's all you'll ever know.
Two is twice as many as one, and three even more.