6th round pick, 199th overall. There is a documentary called the Brady 6 which tells the story of what happened to the 6 QBs that were drafted before him. Yes, 6 teams in need of a QB that year passed on Brady.
Crazy to think now but it ties into the natural ability thing mentioned previous. His numbers and the college he went to, Michigan state, together with his combine scores did not tell the story of what was to unfold.
EDIT: University of Michigan that should read.