Typography is somewhat of a vice of mine. So much so that a 1700 paged FontBook weighs down a shelf of my bookcase. To me, nothing makes or breaks an otherwise class-design than the wrong typeface. While a scholarly, but contemporary, type from the Palatino family is mostly universal in application, something like Terfens will not be perceived as very professional and, in turn, you or your company as not all that serious about business.
Choosing the right typeface is not only about what best fits into your website's aesthetical agenda, but how it reads. A heavy, tight, or widely-spaced type hinders the rate at which a user is able to read your text. It is only suitable for headlines, not the body. Because the speed of reading diminishes onscreen, compared to reading from a book or a newspaper, the transition must be made as seamlessly as possible.
With all of these factors in mind, choosing the right typeface can become a daunting task. If you are considering revamping the type on your site and flipping through the pages of a FontBook is more of an investment than you are willing to make, may I suggest a nifty little utility i recently stumbled upon, UrbanFonts. They offer over 8000 free types for download; and although most of them are slag, there are still a few quality ones floating around.
To gain a better grasp of how redesigning your typeface layout will affect your website, Smiley Cat Web Design Blog provides us with a GQ Magazine example; swapping out a crowded type for one with a bit more space between letters and words. Personally, I'm not a fan of their result. It may be more attractive on page, but it reads slower, and on a medium where the majority of readers are skimming their content, such a hindrance is just not acceptable.