Hey, so I've been reading a lot about Node.js and want to jump in with a quick (multi)weekend project to learn it. What apps would you suggest building to learn the basics and just have some fun?
I'd suggest using Express.js node.js framework: it gets you up and running quickly. Trying to so something with websockets is fun as well and indicative of the (realtime) future of web apps.
GitHub use it for their download server - try running wget against one of the URLs they provide for downloading a tarball, you'll see it redirect to nodeload.github.com, hang for a few seconds (while they generate the file) and then redirect you to the download location.
How about a dead simple document sharing website that lets people read the same doc, on multiple computers, at the same time? (i.e. if you have a bunch of people on a call with computers up, the speaker can send around a reading link that lets him or her flip pages for everyone viewing.) I find myself wishing for this functionality pretty regularly lately. Broadcasting the pointer, real time comments & annotations seem cool too.
I made a Tweet Wall in a day, with Socket.io (for websockets) and TwitterNode (for connecting to Twitter's real-time search API). It was a pretty good intro to the concepts.
I can second this as a good way of learning. The Node.js site links to a very readable long polling chat app here: http://github.com/ry/node_chat. I learned the framework by modifying this into an IRC-style party game am now working on mobile clients for it.