Ask HN: Favorite projects for learning a new language?

My next step up from "Hello World" should be relatively simple for most languages.

Pick a public JSON API. Retrieve it over HTTP. Parse the JSON into a data structure. Print some interesting part of the data.

This exposes you to HTTP and JSON libraries in a new language, as well as working with data structures. For instance, in Go, the parsing JSON step forces you to write some structs and learn about marshalling.

Unless there are significant differences in the way a web framework is structured (i.e. Pedestal for Clojure), I find that making a web app doesn't really contribute much to learning the intricacies of the language.

I like to try out a languages interesting features by wrapping an existing library in an idiomatic style suitable for that language. For example my most recent work is attempting a wrapper around SNMP4j in Clojure, foregoing the OO style for a more data-centric approach.

I have had fairly good results just use it for data/calculation stuff that I need or using it without justification in a side project. Even if what you're working on is in X, do a bunch of your experimentation in Y. It costs more for the side project, but if you're not terribly concerned about the pace of the project then it's a net win. Practice new skills and have a presumably enjoyable task within which to practice them.

I try to replicate a blog with posts, tags for posts, and users. It's a good way to get familiar with the ORM and creating associations assuming you will use relational data. I recently started learning Play Framework (Java/Scala web framework) and it worked pretty well.

EDIT: This is assuming you are intending to learn a web framework along with the language.

Choose your own adventure games seem to be one of the things that I work on for the longest

Whichever project I'm most interested in actually doing at the moment.

Simple games.