Please don’t use underlines as emphasis on the web. That’s just confusing. Underlines should be used for links, nothing else. I think that should be self-evident but some people still get it wrong. Clicking on underlined words – expecting further explanation or additional material – with nothing happening always makes me sad :)
(As an aside, I personally don’t like underlines even in print. I much prefer the subtle use of italics. But that’s very much a question of taste.)
Most style guidelines strongly recommend against using underlines in print. Underlining used is for emphasis in handwritten material, because it's difficult to hand-write italics, much less bold. In a printed context, it just looks... unprofessional.
Of course, this is a stylistic preference and not a normative linguistic imperative, because I detest such things. But it's a very common one.
(As an aside, I personally don’t like underlines even in print. I much prefer the subtle use of italics. But that’s very much a question of taste.)