Yes, in the 21st century, there are still writers who use pen and ink, for their first drafts, at least.

Sam Anderson, a staff writer for the New York Times Magazine, told another writer at the paper that he actually composed the first draft of most of his long pieces by pen. He liked how it slowed him down:

There’s a kind of folk craftiness to it. The first step is a very personal thing — drawing yourself out of your mind and body. Then, later, you translate that into impersonal print…

Anderson also found that the process, even though it was time-consuming and required to be typed up later, was ultimately a time saver because it stopped him from fooling around on the Internet.