Yes, writers have them sometimes.
My favorite sf-writer John Scalzi has a very succesful blog called Whatever. The post that gained Whatever eternal fame?: a photo of a cat with bacon taped to its side. ( No, I am not kidding)
And another favorite of mine is Charlie’s Diary. The blog of sf-writer Charles Stross. Full with reflections about the future of technology by a ( somewhat) grumpy scotsman.
Some writers are more famous as bloggers than as writers. Like Cory Doctorow . He is one of the main bloggers of the biggest Blog on the net: Boing Boing. He also has his own blog called Craphound and, apparently blogs from a high altitude hot air balloon wearing goggles and a red cape.
Technically not a famous writer but who cares when it is Wil Wheaton, better known to the Trekkies as Wesley Crusher! Wil Wheaton has a blog about all things geeky and nerdy called WWdN: In Exile
And some writers claim they do not have a blog, like fantasy author George R.R. Martin famous for his Song of Fire and Ice saga. It’s just something that looks a lot like it: Not a Blog