Its a question I get asked often. NYTimes provides an answer:
For those who want a simple Weblog and do not have a file server to store it on, several sites offer templates and serve as free hosts, for example, LiveJournal (www .livejournal.com) and Blogger (www.blogger.com). For more complex blogs with more customizable features and fewer advertisements, both sites also offer services for $50 a year or less.
You can also buy desktop software programs to create a Weblog. Radio UserLand sells for $39.95 and works with Windows and Macintosh systems. Users receive 40 megabytes of space to store their blogs on the software company’s servers. A trial version can be downloaded at radio.userland.com, and UserLand Software has a Weblog information site at http://www.weblogs.org, which itself is a Weblog about Weblogs.
For diarists with their own Web server accounts, Movable Type has free software for creating a Weblog at http://www.movabletype.org, and Fog Creek Software has a free version of its CityDesk program for Windows at http://www.fogcreek.com/citydesk.