Both are correct, but I think "What sports do you like?" sounds more natural in everyday conversation because most people enjoy more than one sport. With colors, I usually hear "What color do you like?" when someone is asking for a favorite color, and "What colors do you like?" when they're asking about several colors. English can be funny like that. Small changes can slightly change the meaning. I actually came across a few useful language discussions recently while browsing https://pak-guide.blog/.