2005
San Francisco selects Alex Smith #1 and then selects offensive lineman David Baas #33
Green Bay selects Aaron Rodgers #24 and then selects safety Nick Collins #51 (one of the few exceptions, but they did take a wide receiver, Terrence Murphy with their 2nd of their two 2nd round picks)
Washington selects Jason Campbell #25 and then selects running back Manuel White #120 (Why I am not surprised Washington had no mid round picks in 2005? Do they ever have mid round picks?)
2006
Tennessee selects Vince Young #3 and then selects running back LenDale White #45
Arizona selects Matt Leinart #10 and then selects offensive lineman Deuce Lutui #41 (4 years later, Derek Anderson would share a laugh with Deuce Lutui while getting blown out by the 49ers and then explode when asked about it in a press conference)
Denver selects Jay Cutler #11 and then selects tight end Tony Scheffler #61
2007
Oakland selects JaMarcus Russell #1 and then selects tight end Zach Miller #38 (see even the Raiders follow the trend)
Cleveland selects Brady Quinn #22 and then selects cornerback Eric Wright #55 (another exception, but remember the Browns had just taken offensive lineman Joe Thomas #3 overall)
2008
Atlanta selects Matt Ryan #3 and then selects offensive lineman Sam Baker #21
Baltimore selects Joe Flacco #18 and then selects running back Ray Rice #55
2009
Detroit selects Matt Stafford #1 and then selects tight end Brandon Pettigrew #20
NY Jets select Mark Sanchez #5 and then select running back Shonn Greene #65
Tampa Bay selects Josh Freeman #17 and then defensive tackle Roy Miller #81
2010
St. Louis selects Sam Bradford #1 and then selects offensive lineman Rodger Saffold #33
Denver selects Tim Tebow #25 and then selects offensive lineman Zane Beadles #45 (they also selected wide receiver Demaryius Thomas #22)
2011
Carolina selects Cam Newton #1 and then selects defensive tackle Terrell McClain #65
Tennessee selects Jake Locker #8 and then selects outside linebacker Akeem Ayers #39
Jacksonville selects Blaine Gabbert #10 and then selects guard Will Rackley #76
Minnesota selects Christian Ponder #12 and then selects tight end Kyle Randolph #43
2012
Indianapolis selects Andrew Luck #1 and then selects tight end Coby Fleener #34
Washington selects Robert Griffin #2 and then selects offensive lineman Josh Leribeus #71
Miami selects Ryan Tannehill #8 and then selects offensive lineman Jonathan Martin #42
Cleveland selects Brandon Weeden #22 and then selects offensive lineman Mitchell Schwartz #37 (they also selected running back Trent Richardson #3)
So all in all, of the last 19 teams to draft a quarterback in the first round, 14 of them drafted an offensive player with their very next pick. Of the 5 who didn’t, one drafted an offensive player with the pick before the quarterback and one drafted an offensive player with the 2nd of their two 2nd round picks.
