KGYSAK - 좋아 vs 좋아해요

Why does this one confuse me? Well, it goes back to the whole subject versus object discussion. If it's a subject, use 좋아. If it's an object, use 좋아하다. Try not to think of it as "if you like the subject" or "if you like the object" because that's a bit misleading. Plus, one type of thought can easily be expressed a number of different ways. For example:
소녀시대 중에서 누가 제일 좋아?
소녀시대 중에서 누구를 제일 좋아해?

Both loosely mean "Who is your favorite member in 'Girl's Generation'?" but one uses 좋아 and the other uses 좋아하다. Confused? As simple as it is, I get it messed up from time to time. I shouldn't but I do.

A trick that might help is to think of the root. 좋아하다 is a 하다 verb. 하다 is to do something. If you like to do something, then it's 좋아하다 as in "운동 좋아해요?" (Do you like to exercise?) makes more sense than "운동 좋아요?" which makes virtually no sense. If you want to ask if someone likes the act of exercising, perhaps what you mean to ask is "운동 하기 좋아요?" which would, to my best translation, be the same as I the first example but only less common.

Lastly, I've once heard the explanation that 좋아하다 is only used for active verbs but I couldn't tell you the first thing about active versus non-active verbs let alone verify if that trick actually works.

UPDATE: TTMIK has a great lesson on this very subject