As other answers have pointed out, the amount of memorization required varies course to course and institution to institution. I thought it would be helpful to provide some examples:
1) First midterm exam in the intro CS course at Princeton (this is usually the first exam CS students will take)
2) Final exam in the "Algorithms and Data Structures" course at Princeton. This is usually the second or third course a CS student will take.
Again, note these examples are only from a single institution in the US, but hopefully they provide a little insight into what CS exams are like at the undergrad level.
Note: both of these exams are closed-notes, but in each case you were allowed to bring in a one-page "cheat sheet"