Probably the most important classes are upper-level math classes. If your school offers calculus, by all means take it.
Engineering is a math based subject.
Physic and chemistry are also basic science classes that will apply to engineering. I wish I had taken in high school was typing. Today's engineer will use a computer and the need to know typing is needed as well. On that same line, learn all you can about computers as well. Argonne National Laboratory, Division of Educational Programs, Harold Myron, Ph.D., Division Director.