The main benefit to Wordpress is its built-in content editing system that's mostly accessible to end users. So you can build a site for someone and then show them how to use the nice admin interface and page editor, and let them manage the content themselves after you're gone, rather than having to be involved for every little page change afterward.

And of course as others have mentioned, the plugins are pretty great too. A client can ask you if you can do X (e.g., tie into their Twitter) and BAM, install a plugin, done, you look like a hero. Compare that to having to write/install/test something similar.