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How do you define "simple"? Say, I'm learning C or C++. Writing a Tetris clone as the first project wouldn't be very obvious/straightforward, but neither of those languages is a toy.
It'd be obvious and pretty straightforward once you understand how Windows or Qt or whatever does things. (That'd be a prereq for any low- or mid-level language: knowing how to use the underlying system. Even some high-level languages require that.) And Visual Studio (and AFAIK most other IDEs) will create a bare-bones C or C++ app for you, so you can basically just work on the code to run the actual game.
"hello world" is overdone (just about every book about the language already includes it!), and doesn't give a decent language any real workout. I don't really get a feel for the language til i've done something non-trivial with it (which requires that i go and figure out "ok, this is how you do timers...this is how you watch the keyboard"...etc.)
I like to do some I/O exercises(both file system and console), then a text adventure game, because it helps me understand the way data structures are used in that language (it really helped when I was working on Lisp). They're also fun to make.
I Google for a tutorial on the language and follow that, usually. If there isn't one somewhere on the language's website then that's not a great sign. More often than not, I've looked up some examples before even downloading the language toolkit in order to get a feel for what to expect (there's so many languages popping up that you can't hope to try them all, so best to stick to languages with features you find interesting).