Your choice of typeface is second only to your choice of color in the impact it has on your user.
Selecting the right typeface for logos, slogans, titles is extremely important in showcasing the qualities you want to project for a particular client.
It is also important to take into consideration the typeface and design for your copy.
Often on the web it is as if the designer loses interest once they get to the the section of the content which is primarily text. On some sites very little effort is given to making the design of the copy visually interesting.
All sections of the web page including the copy needs to be designed to keep your user's interest.