We do! A lot of our client-side tools are written in JavaScript, and run in Node, especially now that Node is a pretty ubiquitous tool for developers to have on their laptops.
For example, Remodel (https://github.com/facebook/remodel) is a tool for auto generation of model classes for iOS, and it's installed via npm.
Also, all of our internal GraphQL client side tools for iOS and Android at Facebook use Node and are built on top of graphql-js (github.com/graphql/graphql-js).
We're not using Node much on the server side of things, but mostly because there hasn't been a serious need. Between our services built in C++, and our application server in Hack, we're pretty well covered.
There have actually been a few cases where we've run JavaScript on the server, mostly to do some server-side rendering of React components, but for those we actually haven't used node and instead used v8 directly.