"What kinds of houses do you like?"
Translation:Milyen házakat szeretsz?
No, it should not. However, both "what kinds" and "what kind" should be accepted as English translations.
Perhaps you could expand? What would the sentence mean with "milyenek" in place of "milyen"? I am a bit vague on the difference between pluralized and non-pluralized adjectives and similar, and would like to understand better.
Milyen behaves like adjectives behave in Hungarian: when it's modifying a noun, it doesn't take any plural or other endings, even if the noun is modified. So, for example, all of the following are correct:
Ez egy szép ház. (This is a beautiful house)
Ezek szép házak. (These are beautiful houses. Házak is pluralized, but the adjective remains unmodified.)
Látod azt a szép házat? (Do you see that beautiful house? Here the object házat has the accusative ending, but still the adjective szép remains unmodified)
Milyen behaves the same way:
Milyen ház ez? (What kind of house is this?)
Milyen házak ezek? (What kind(s) of houses are these?)
Milyen házat látsz? (What kind of house do you see?)
In each sentence it's the house (or houses) which are playing the subject or object role, and milyen is a modifier.
You will only use milyenek (or other declined forms of milyen) when it is functioning as the subject, object, or predicate in its own right. Same with adjectives. This maintains a nice kind of parallelism, since "milyen" questions are generally answered with adjective answers, and the form of "milyen" should match the form of the adjective you would expect in the answer. Examples:
Azok az almák pirosak. ("Those apples are red", or "those apples are red ones" - the adjective is the entire predicate.)
Milyenek azok az almák? (What are those the apples like?)
-Nyuszikákat látok. (I see bunnies!)
-Milyeneket látsz? (What kind do you see?)
-Aranyosokat látok! (I see cute ones!)
(Fair warning, I'm not a native speaker so you might want to take all that with a little caution, until a native speaker has a chance to contribute.)