Both with 都 or without are right. It really depends on the context. Here I want to talk about the case with 都. When we ask that question, there are two situations: 1) I would be implying: what sports do you EVEN like? I might be talking to someone who's really not into sports. I might be asking him/her to go play some sport with me but got a 'no' no matter what sport I suggested. Possibly with a big frown. 2) I assume that there are more than one sport this person likes. This sentence can be translated as: What are ALL the sports you like? But then it would be more appropriate to say: 你都喜欢哪些体育项目？Using 些 in stead of 种 to assume there are more than one answer.