When relaunching my personal site, I wanted to import the few posts that I had made on http://e2jk.tumblr.com/. As all programmer/computer geek will tell you, we are lazy people: copy/pasting content from the web browser to text files was just not an option!
I found a project called Edison that does the bulk of what I was looking for: create one .rst files for each Tumblr blog post. The project had a couple of issues with encoding and non-Youtube videos, so after a bit of hacking I got the project working for my use case (note: you will need to generate an API key from Tumblr).
A bit of manual processing was needed (namely to get the hyperlinks and lists working), but it was overall a very useful project.