Not a lot of Punters get drafted, but Reggie Roby did in 1983 when the Iowa Hawkeye was chosen in the sixth round.
The twin brother of Maurkice Pouncey was also an NFL Center, and while he did not become an All-Decade team member, he was a very good player in his own right.
Tim Ruddy played his college ball at Notre Dame, and the Miami Dolphins used their Second Round Pick to select him in 1994.
A National Champion with Alabama in 1978, Tony Nathan was drafted by the Miami Dolphins in the Third Round the year after.