You can always use WordPress.com with domain mapping, as explained here:
But you won't have as much control over your own themes, plugins and presentation as you would on a self-hosted blog.
C'mon, man, web hosting is dirt cheap these days. If you sign up with Dreamhost and use one of their codes, you can get a year's worth of hosting for less than the price of a mildly fancy dinner for two.. about $27. :)
Surpass Hosting (which I highly recommend) has packages for as low as $6/month, pay as you go.
Also, who is your Internet Service Provider? They sometimes have free space for their account holders. You can't always attach a domain to it (well, not EASILY), but it can be done sometimes.