1. What do you not like doing?

2. What don't you like doing?
3. What do you hate doing?
4. What do you dislike doing?
-I don't like doing computer games.

(Which questions are commonly used? Are all grammatical?)

3 answers

They are all correct. I think 4 is best, though.
All 4 are grammatically correct, but #1 isn't used much. The others are more commonly used.

You should use a more specific verb in the answer: I don't like playing computer games.
What do you not like doing?