Pace University is offering a free 12-week Desktop ArcGIS course this fall. It starts on August 27th and ends before Thanksgiving.
The syllabus for the course can be seen here:
http://webpage.pace.edu/MMinnis/GISSyllabus/ There is a FAQ at the bottom of the Syllabus.
To enroll in the course, go here:
Electronic badges can be earned (bronze, silver and gold) at milestones along the way. People who finish the course receive a certificate.
The instructor is:
Peggy Minnis (MMinnis@Pace.edu)
Pace University - Pleasantville, NY