You can ask like this (どんな音楽が好きだ?), but it does imply rather masculine way of asking this question. It is informal as well.

どんな音楽が好きですか? Is a more polite/formal way of asking the question, probably appropriate for people you just met or someone you respect (ie., teachers).

どんな音楽が好き？Is probably a more natural, colloquial way of asking that question towards a friend.

Let me know if you have any questions! 

How to ask about music?

Is it possible to ask this question this way?
どんな音楽が好きだ。
Or is it necessarily どんな音楽が好きですか。 ?

よろしくお願いします。

どんな音楽が好きですか？　is correct.

If you want to ask casually, you can ask like どんな音楽が好き？

音楽が好きだ、　is a casual definition form,  so you can't use for a question and not polite.

When you are talking to your friend, you can say,

わたしはこの音楽が好きだ！