Fantastic resources on explaining when it is right to use Node.js. The overall consensus is you use it when you need live / updating content on a page. The main issue Node can really tackle is and issue called "Long Polling". This is when a person is connected to page and the server is constantly updating that page. The key example mentioned would be a chat program. A user connects to the page and it is constantly being updated. In the past this would be a resource hog with a user taking up a thread on the server cpu. Node.js frees up the resources and opens up possibilities with regards to socket handling. This is great for in-browser applications as well as multiplayer games and such.
Node.js is also getting some notice as a webserver because of its ability to handle data through MYSQL and JSON. It is the new hotness.