Harmony

When the type is poorly chosen, what the words say linguistically and what the letters imply visually are disharmonious, dishonest, out of tune.
—Robert Bringhurst, The Elements of Typographic Style

Typefaces have character and personality. They can be stately, reserved, bold, flashy, whimsical, romantic, or humorous. They can evoke a bygone era or some imagined future:

Typefaces: Broadway, Comic Sans MS, Courier Std, Edwardian Script ITC, Gigi, Jokerman, Rosewood Std, Times New Roman

When a typeface is in harmony with the meaning of the words, the reader's focus is drawn to the message, not the type. For example, Gigi is obviously inappropriate for the title of a serious philosophical treatise:

"The Meaning of Life" in Gigi

The same typeface, however, would be perfect for the title of a light romantic comedy. On the other hand, there may be situations where you will want to use a disharmonious typeface (for example, to set an ironic tone):

"The Meaning of Life" in Jokerman

Regarding (X)HTML text, the user or the user's computer system can make the question “Which typeface would be the most harmonious?” moot: The typeface that you have so carefully chosen may not exist on the user's operating system, or the user might just have a thing for Times New Roman and might have configured the browser to ignore your specifications.

Nonetheless, you should strive for harmony, while accepting that you cannot totally control what every user sees. Since this sometimes benefits or even pleases the user—if Mary likes large type in Times New Roman, why shouldn't she get it?—this is not always a bad thing.