Typography is an important aspect of web design just as it is in any other form of print.  Your text should always be appealing to the eye and easy to read.  This goes for any medium you are using ie; web design, posters, business cards, post cards etc.

Anywhere text is used, it’s style needs to be adjusted to suit the medium being designed for.  Publishing, packaging, television, signage etc. are all different mediums that use different formats and therefore need to be adjusted to accordingly. .

A format that works for a magazine would not work the same in poster format.  Magazines are read more closely to the eye, while posters typically are noticed from a further distance so size, spacing and colors all become a factor in the design.

Web design is an issue all its own.  Your typography has to be compatible with multiple computer formats, screen sizes, internet browsers and a laundry list of other potential problems.  As a designer, it is your job to address these issues, understand the problem and maintain a sense of control over what you use and how you use it in your medium.