What models of fax machines use laser fax toner instead of ink?

Many printer manufacturers provide laser fax models or offer fax cards as an accessory for their laser printers. Canon, Brother, Hewlett-Packard, Panasonic, etc. Google "laser fax".

There are also thermal type fax machines that use heat directly to imprint the image in special paper or use heated ink. See HowStuffWorks - Introduction to How Thermal Fax Machines Work.