The only time you need a comma before the and in a list, is when there might otherwise be confusion. In your case, no comma is required.
A more elaborate list might tend to be confusing, so a final comma helps clarify your meaning:
Yesterday I ate ham and eggs, toast and jam, and beef stew.
You need that final comma to clearly differentiate the three menu items.
It is not necessarily wrong to use a final comma even in a simple list, however. Simply unnecessary.
If you mean all the students' names, then you
remember the names of the students in your class
If you only remember a few of them, you might say that you
remember the names of students in your class, or even
remember names of students in your class.
The last one (without any article) sounds a bit more vague, as if you were almost dreaming, remembering, memories fading in and out as you do. "I remember names of students, falling leaves, a distant bell...."