General:
* Student
* Learner
* Pupil (more common for younger students)
* Scholar (more formal, often used for university students)
* Disciple (used in religious contexts)
More specific:
* Undergrad (for undergraduate students)
* Grad (for graduate students)
* High schooler
* Elementary schooler
* College student
* University student
* Freshman (first-year student)
* Sophomore (second-year student)
* Junior (third-year student)
* Senior (fourth-year student)
Informal:
* Kid
* Kiddo
* Student body (refers to the entire student population)
The best word to use will depend on the specific situation.