If they're marked up well in a page they can be beneficial for SEO, or used as a short summary of the expected content of the website/purpose of the business.
A lot of website use them in the page title as well as being displayed in the header: Page name | Site: Tagline
Some examples:
- Smashing Magazine — For Professional Web Designers and Developers
- The Next Web - International technology news, business & culture
A lot of website use them in the page title as well as being displayed in the header: Page name | Site: Tagline
Some examples:
- Smashing Magazine — For Professional Web Designers and Developers
- The Next Web - International technology news, business & culture
Some interesting articles:
- http://www.onextrapixel.com/2013/01/14/effective-website-tag...
- http://www.simplewebsiteservice.com/how-to-write-a-tagline/
- http://www.toprankblog.com/2009/07/blog-taglines/
- http://intuitivewebsites.com/articles/website-taglines/