I was looking for an easy way to make a development copy of the Many Tricks blog, which (like Robservatory) is powered by WordPress. In the past, I've done this manually, but it's a bit of a pain to get the required edits done correctly and make everything work at the new URL.
So this time, I went searching for a plug-in, and found Duplicator. Borrowing from the plug-in's description of itself…
Duplicator gives WordPress administrators the ability to migrate, copy or clone a site from one location to another. The plugin also serves as a simple backup utility. Duplicator supports both serialized and base64 serialized string replacement. If you need to move WordPress or backup WordPress this plugin can help simplify the process.
Once installed, usage is pretty easy: You follow a simple three-step process that creates a new package. Move that package to the new location, expand it, and then run the installer.php file. (I had to rename the three files from the package to remove everything except the filenames; the plug-in adds a bunch of identifying text in front of each filename.)
The installer asks questions about the new site's URLs and database connection info, then does its magic. I had a clone site up and running in minutes, saving what (for me) is usually an hour or so's aggravation. Duplicator should work equally well for moving a WordPress installation to a new host, too, though I haven't tested it in that situation (yet).