Students in a particular grade are called formers. For example, there were 20 applicants admitted as Fourth Formers at Groton School for the academic year 2008-2009.
The usage comes from English private schools such as Eton - or as the British call them public schools. In the U.S. you will encounter the use of form, as opposed to grade, in the older, more tradition bound prep schools. It is less commonly used in newer private and independent schools.
Find more terms in the Private School Glossary.