There are many famous brands using WordPress. Sony Music, Renault, Vogue, Facebook, The New York Times and the BBC. There is an excellent Showcase page on the WordPress site that features many of the great sites using WordPress.
A favourite of mine is Facebook’s Company info page, in which Mark Zuckerberg is just another humble CEO, on just another humble About Us page on the internet. Sheryl Sandberg even mentions her fish.
So with around 20% of the internet, and 70% of the CMS market, and growing, if you are not already using WordPress, you really ought to, come your next new website.