I always believed that when starting to learn a new programming language programmer must create certain projects to get a better understanding of the language and/or frameworks. Personally for me it was with php (guestbook, DB abstraction, templating engine), ruby (on rails, twitter like website, active record plugin, simple gem) and objective-c (cocoa, todo-list, twitter client).
I'm wondering what are the must-program projects for other programming languages like Java, C++, Python, etc? Maybe you had other path learning languages?
The first 20 or so are nice small problems that let you experiment with languages basic execution control stuff. Gives you a good feel for how a language operates in the 'small'.