Well, one could write a rather lengthy essay about this, and I am sure many have ... For the web, there are two possibilities: stick with the system fonts (Arial, Helvetica, Times, Georgia), or use a web font (@font-face) for display. No real alternatives, because a font on screen has to have good hinting. No use choosing a classy typeface that people tire of seeing on their screens.
For printed material there are also many things to consider: Does the typeface have all the glyphs you need, say, for writing in foreign languages if needed, or setting foreign names? Does it go with the wordmark? Does it match the company’s identity? Is it well designed (not too many around that fit this description)?
For a good read on typography and typefaces take a look at Robert Bringhurst’s Elements of Typographic Style. I do not cease to be amazed by this insightful book.