In the World Wide Web, the hyperlinks are often underlined and shown in color different from the rest of the body text.
There were a few different other ways of noting the links earlier; Some browsers used boxes around the links, for example. The first browser (IIRC) to do the link emphasis this way was Mosaic, also being the first really popular web browser. Netscape Navigator followed this trend, and so did the Mosaic-derived browser, Microsoft Internet Explorer. The rest, as they say, is history.
Surprising amounts of graphics people are thinking these days that link underlining in the Web is a bad thing, and eagerly took CSS (along with other cool stuff it offered) and remove the link underlinings with it. Great confusion ensued.
The links still should still be underlined. Why? People have got used to it. Plus, it's also pretty damn clear way of showing that something is linked. So, why change the estabilished convention?
Let's first consider what underlining means these days. Underlining was used previously in low-typography world (typewriters etc) to denote emphasis. However, in the age of graphical and semigraphical computer displays, people should use italics and bold to emphasise important things. Underlining as an emphasis makes text harder to read, while bold will not harm anyone too much.
However, people have these days grown to think "oh, that's underlined and it's of different color as the main text, so it has to be a link." Try to toss them some text with just randomly colored words, and it might take them few moments to get hang of this strange behavior.
The worst offenders in the underlining eradictation camp remove the underlining and the coloring from the link, only adding "hover" color (so the link can be seen when the mouse pointer is on the link). Good hunting, folks.
Of course, it's possible to remove the by-default link underlining from browser settings (at least Mozilla/NS support this), but it's pretty hard choice if you have already got used to this...
...Bottom line: Let people choose themselves if they want underlining or not. Don't take away the underlines we want.