Which tense to use depends on your meaning, i.e. what information you want to express. In the simple case, when Amy is currently a student, then John is correct. But, if Amy was a student who left school, then past tense is possible. e.g. Amy is now a university student, and her high school teacher is talking about her, then 'Students such as Amy liked reading books'. It's even possible that if Amy is a student in a school in a poor country, and someone has just built a library, that she will be soon able to use, then 'Students such as Amy will like reading books'. There are even more complicated possibilities with more complicated tenses.

Hi Iris, you would use the present simple (plural singular) here...Students such as Amy like reading books. The subject in the sentence is "students" (they).