Well, from the Polish point of view, such usage of "like" is completely different.
The closest would be "Co chciałbyś/chciałabyś?" (male/female, conditional is based on the past tense form, so it shows the gender of the subject), also it would make sense to use some verb in the infinitive, to specify what you mean. This would be translated into English as "What would you want?"... if only this was correct in English.
An alternative, which is easier in use is "Na co masz ochotę?" - something like "What do you feel like (doing/eating/drinking/etc.)?"
Or conditional "Na co miałbyś/miałabyś ochotę?".
Thank you -- it's true that even in English "what would you like?" makes no sense by itself, and only works because it's an idiomatic abbreviation of "what would you like (to have/eat/drink) (for your birthday etc)?", and even then only in the appropriate context.
It is also more courteous the the blunt "what do you want?" and I wonder if Polish makes that distinction with your examples: "Na co masz ochotę?" vs "Na co miałbyś/miałabyś ochotę?".
cheers -- Simon
It depends mostly on the verb, and it's easiest to see when you imagine the answer to the question.
"co" is either Nominative (Co to jest? To jest kot. = What is this? This is a cat.) or Accusative (Co jesz? Jem zupę. = What are you eating? I am eating soup.) You can for example see that the verb "jeść" (to eat) takes a direct object in Accusative, that's why Accusative "co" is used.
"czego" is Genitive, e.g. you can have "Czego szukasz? Szukam chleba." = "What are you looking for? I am looking for bread." - the verb "szukać" takes Genitive, which here is "czego".