Eric Crouch
The 2001 Heisman Trophy winner was thought to be a better wide receiver than a QB. The St. Louis Rams took him in as a third-round pick in the 2002 draft. However, he did not see a down in a regular season. He joined a couple of teams and leagues during the course of his career. Aside from the NFL, he was also safe for the Hamburg Sea Devils in NFL Europe. He also played QB with the Argos in the CFL.
Jason White
In 2003, Jason White won the Heisman Trophy. He went on to lead Oklahoma to back-to-back National Championship Games. Even though he had a great track record in college, the team lost both games. He was not picked for the NFL Draft and did not receive tryouts from any team during the first few weeks after the post-draft free agency of the NFL. This made him the third Heisman winner who was not drafted in the NFL. The ones that came before him were Pete Dawkins and Charlie Ward.