Here's a short guide to setup a Mercurial repository in a DropBox folder. You'll need a DropBox account set up and Turtoise Hg installed.
First, create a DropBox folder for your Hg repository. I've got a project called Places, so I created a directory ./Projects/HGRepositories/Places
Inside your project directory, right click anywhere, then go TortoiseHg->Create Repository Here
Follow the instructions. The destination directory should be the same as the one with your project.
After you've finished initializing your repository, you should have the .hg folder and the .hgignore file added to your directory.
Set up the ignore list.
Copy the entire project directory over to your DropBox directory
Next, from your project directory, open the Hg Repository Explorer.
From the Repository Explorer, Commit your project.
Now, push your changesets to the DropBox repository.
And there you go. Your repository now has backup and is available from any computer that has access to your DropBox folders. In order to check out at another computer. Create an empty folder. Inside it, right click and choose TortoiseHg->Clone and clone the repository from the shared DropBox folder.