Saving Weblog

The clumsy approach (making a 1:1 clone):
wget does it. If you just want the public part, i.e. everything a visitor would see, this is trivial and can also be done with a dozen other programs. (What have you tried? E-mail clients or something?)

If you want to spider everything as an admin in order to get offline stories and stuff, you have to make wget send the appropriate cookie, which is not-so-trivial. I succeeded when I tried that out once, but I don't want to publish that solution because it's really clumy. For example, it downloads the edit and reply form and everything for every single story and is generally quite redundant and strains the server. But if you're interested and can't get it to work yourself, tell me and I'll have another look at it and try to come up with something better.

The clever approach (downloading just the content):
Use the RSS feed, there's surely software to take care of your problem that way. Unfortunately, I don't know jack shit about RSS; maybe someone else can help.