The term "desktop publishing" usually refers to the process of creating and printing out a document from one's computer; "desktop publishing" is generally held to have begun when, especially on the Mac, computer users were first able to pick out fonts for a document and print that document from the comfort of their homes and offices. No longer was publishing limited to those with access to a printing press!

But actually, students, secretaries, and other amateur typographers had been producing print documents from their desktops for nearly a century before the term "desktop publishing" was coined. They used a little device called a typewriter.

The typewriter, unlike the printing press, was a one-trick pony. It had one monospace font, in one size, one weight, one style. Typewriter text was less typographically expressive than traditional printed text that could be kerned and italicized; the lack of italics was a particular problem. How to indicate emphasis for a word, or properly style a book title in a citation? Typewriters borrowed a convention from editors' proofreading markup: an underline indicates "this should be italicized". Underlines were easy enough to add to typewriters, and so all the style manuals written for twentieth-century typists indicated that an underline was the proper way to indicate a title, or to add emphasis.

Meanwhile, the typewriter's monospace font made the space between sentences no larger than any other space in the text; in printing, the proportional font allows for a slightly larger space at the end of a sentence. And so another hack was developed for typewriters: when you come to the end of a sentence, put two spaces after the period rather than just one. This and many other typewriter-specific rules became standards in style manuals, and in the age of the typewriter, they were the best solution available for the student or office worker who wanted to be able to produce readable documents from a relatively cheap, mechanical desktop machine.

At first, computers only printed out monospace characters, and the old typewriter customs still made sense. But upon the advent of so-called "desktop publishing", the typist could also act as the typographer; and unless you had some sort of sick Courier fetish, you would design and print your documents with the full benefits of a proportional font that had an italic, or at least an oblique, style available. Goodbye, extra spaces! Goodbye, hideous underlines!

Technology emerged from the dark ages of the typewriter, but many typists have not. Those who learned to type on a typewriter, or who learned to type in the old style of the typewriter, have these peculiar habits. They double-space after a period, they use underlines, they attempt to center text with tabs and spaces, they feel an urge to hit 'return' at the end of each line. And if they are designing proportionally typeset paragraphs, they are wrong.

Putting two spaces after a period, in a proportional font, is unnecessary and in some fonts may make the text harder to read (although in HTML, unless you have a cruel WYSIWYG editor that adds extra non-breaking spaces, your double space is mercifully converted to a single one). Underlining disrupts the appearance of text, impairs readability, and sends typographers and graphic designers into fits of agonized screaming. ("The ugliness! The ugliness!")

On the web, the underline has a special purpose: identifying links. Not everybody uses underlines on their links, of course, but it is a widely recognized convention. For this reason, the underline is acceptable to some people who otherwise would hate it; but more importantly, underlined text that is not a link is very confusing, and should be avoided for this reason as well. For the moment, I'll ignore the other differences between printed and nscreen text; there are other factors that come into play. But for a general guide to un-learning typewriter conventions to make for better computer typography, check out A. Cemal Ekin's Typewriter Days: A Bygone Era That Won't Go Away (pdf) at http://www.providence.edu/mkt/ekin/toptips/layout_guide.pdf

further reading:
http://www.webword.com/reports/period.html