Since Steve Young it's been
1986 Robbie Bosco (3rd rounder, #72, Green Bay)
1992 Ty Detmer (9th round, #230, Green Bay)
1995 John Walsh (7th round, #213, Cincinnati)
2002 Brandon Doman (5th round, #163, San Francisco)
2007 John Beck (2nd round, #40, Miami)

If you're a quarterback taken outside the first round it's very unlikely you make an impact. There's a few exceptions, but it's hard to be a big disappointment there. The closest is Beck who was drafted early in the 2nd, was the 3rd stringer before being forced into the starting role for injuries and didn't play well. He still had a 6 year career as an NFL backup which I'd guess is about par for a 2nd round QB). The QBs taken ahead of him that year were JaMarcus Russell, Brady Quinn and Kevin Kolb, so it's hard to look at Beck as a terrible QB pick where he went. Either Beck, Kolb or Trent Edwards was probably the best QB in that draft class - just ugly all around.

Otherwise, Detmer, Doman, and Max Hall (UDFA) did quite well considering where they were drafted.