"Why are you not coming?"
Translation:Varför kommer du inte?
Well, "inte" is a sentence adverbial ("satsadverbial" in Swedish) and in a main clause it comes directly after the verb:
Du kommer inte.
In a question, the pronoun and the verb change places:
Varför kommer du inte?
Here, "inte" is negating the whole sentence, but if you want to stress "du" (Why are the others coming but not you?), you can ask
Varför kommer inte du?
In a subordinate clause, the sentence adverbial must be placed before the first verb:
Han undrar varför du inte kommer.
English used to have more flexible word ordering. We still use the flipped ordering in questions and other cases, but it's often the auxiliary verbs, like to do, that end up at the front: "Why do birds fly?"
Wikipedia has an article on this: http://en.wikipedia.org/wiki/V2_word_order