The email service available at no cost to students, faculty and staff as a part of the university's standard computing services is Google UMICH Mail. This is one of many Google Apps provided to the U-M community. (see M+Google for details)
Some U-M schools, colleges, departments, and units—such as the Health System—offer alternative email services to their faculty and staff, and sometimes to students as well. Check with your departmental administrator for more information.