The History of Weblogs
My name is Dave Winer and I run the Scripting News weblog, which was one of the earliest and is currently the longest-running weblog on the Internet.
Weblogs are often-updated sites that point to articles elsewhere on the web, often with comments, and to on-site articles. A weblog is kind of a continual tour, with a human guide who you get to know. There are many guides to choose from, each develops an audience, and there's also comraderie and politics between the people who run weblogs, they point to each other, in all kinds of structures, graphs, loops, etc.
Today, there are hundreds of thousands of weblog sites, and the market for tools for managing such sites is growing quickly. My company, UserLand, makes two products for weblogs, Manila, which is a centralized server-based content management system; and Radio UserLand which provides easy and powerful weblogging from the desktop.
Early weblogs 
The first weblog was the first website, http://info.cern.ch/, the site built by Tim Berners-Lee at CERN. From this page TBL pointed to all the new sites as they came online. Luckily, the content of this site has been archived at the World Wide Web Consortium. (Thanks to Karl Dubost for the link.)
NCSA's What's New page took the cursor for a while, then Netscape's What's New page was the big blog in the sky in 1993-96. Then all hell broke loose. The Web exploded, and the weblog idea grew along with it.
I did my first weblog in February 1996, as part of the 24 Hours of Democracy website. It helped glue the community together, along with a mail list that was hosted by AOL. In April 1996 I started a news page for Frontier users, which became Scripting News on 4/1/97.
Other early weblogs include Robot Wisdom, Tomalak's Realm and CamWorld.
Personal Web Publishing Communities
Viewed another way, weblogs are Personal Web Publishing Communities. 11/16/01 DW.
News stories about weblogs
3/8/00: E&P. "Slow corporatization of the concept will probably be fine with many of the thousands of independent Webloggers who pioneered the concept. Romenesko says as Weblogging becomes more widespread among corporations, there's likely to be some resentment from the pioneers who see it as an anti-corporate concept."
2/23/00: Wired. "Thanks to new easy-to-use software, the number of weblogs on the Net seems to be growing at an unprecedented rate."
9/7/99: Chicago Tribune. "A Weblog is a Web site that maintains a constantly updated list of links to other sites; those links can deal with any subject or focus on a particular one. Webloggers typically offer pithy, sarcastic commentary about the links."
8/2/99: New York Times. "Summaries of news predate the Internet, of course. But in the digital era, when virtually anyone with Net access can operate an electronic clipping service, the genre has spawned thousands of news hounds -- not to mention the news links on big portal sites like Yahoo and Excite. Yet, largely through grass-roots, word-of-mouse popularity, sites like Romenesko's are catching on with a discerning crowd -- including reporters and editors of many news organizations, who rely on the sites to help filter the welter of information on the Web."
5/28/99: Salon. "Weblogs, typically, are personal Web sites operated by individuals who compile chronological lists of links to stuff that interests them, interspersed with information, editorializing and personal asides. A good weblog is updated often, in a kind of real-time improvisation, with pointers to interesting events, pages, stories and happenings elsewhere on the Web. New stuff piles on top of the page; older stuff sinks to the bottom."