Learn German: Was wünschst du dir? - What do you wish for?

Because the sentence already has a direct object: the question word Was (What). When a reflexive verb has a direct object (the thing you are wishing for), the reflexive pronoun shifts to the dative case. You can think of it as literally asking, 'What do you wish for yourself?'

In English, we say 'wish FOR'. Why isn't there a word for 'for' in this German sentence?

The German verb sich etwas wünschen doesn't need a preposition. The reflexive pronoun dir already handles the idea of wanting something 'for yourself'. Adding a direct translation like für would be grammatically incorrect here.

Could I just ask 'Was wünschst du?' and leave off the dir?

Not in this context! When talking about wanting a gift or a specific outcome for yourself, you must use the reflexive phrase sich etwas wünschen. You only drop the reflexive part when you are wishing something to someone else, like in the phrase Ich wünsche dir ein schönes Wochenende (I wish you a great weekend).

Why does dir come at the very end of the sentence instead of right after the verb?

In a German question, the conjugated verb (wünschst) takes the second position right after the question word (Was). The subject (du) must stick immediately next to the verb, which naturally pushes the reflexive pronoun (dir) to the end of this short sentence.