Knytt Stories is a free platformer style game in which the main goal is exploring. You don't collect coins or kill monsters, but you collect abilities along the way that let you better avoid monsters and that let you explore more areas (a bit like Zelda in that respect). And it's free and has a pretty usable user-created content system. Oh, and the music is lovely and the graphics are pretty and pixely and the player character is a fairly gender-neutral (only made of a few pixels, after all) female. This youtube video has a fairly in-depth look at it, including a bunch of gameplay video (though I think the video's narrator is a little annoying).