The following write-ups are from Andre Vergara of Fox Sports in 2017.
Additional info was added from Wikipedia.
Chad Pennington, Jets, No. 18 overall
Pennington was the first quarterback taken in a weak class of QBs.
He set school records throwing to Randy Moss at Marshall, and once he took over for Vinny Testaverde in New York, he set team records throwing to third-round pick Laveranues Coles.
Pennington led the Jets to the playoffs three times — his six postseason starts set a team record — before being replaced by Brett Favre.
He battled back from several shoulder injuries to win Comeback Player of the Year twice, including in 2008 after joining the Dolphins and leading them to the playoffs; he finished second to Peyton Manning in MVP voting that year, yet never made the Pro Bowl in his career.
Pennington's 66 percent career completion rate is among the all-time best.
However, he had the misfortune to play his entire 11-year career in the AFC East against the Pats. Pennington was 2-7 in his starts against Brady, completing 63 percent of his passes for 228 yards per game — slightly better numbers than Brady (62%, 209.6 ypg), but the Pats star had the better TD/INT ratio (12/4, vs. 10/10 for Pennington).
On March 31, 2011, he tore his ACL while playing a game of pick-up basketball.
His pro career ended there.
Giovanni Carmazzi, 49ers, No. 65
Carmazzi was a NorCal kid like Brady, and he set school records at Hofstra but was beaten out for the Niners’ backup job by seventh-round pick Tim Rattay.
Carmazzi never took a regular-season snap in the NFL and played in Europe and the CFL.
Brady, meanwhile, held a grudge that his hometown team passed him over.
He last played professional football in 2005.
In an ESPN documentary on Tom Brady released in 2011, it was reported that Carmazzi was then living in northern California as a farmer, yoga practitioner and an owner of five goats. He reportedly did not own a television
Chris Redman, Ravens, No. 75
Redman set school records at Louisville and won the Johnny Unitas Award as a senior after becoming the first Division I-A QB to complete more than 1,000 passes.
Drafted in the third round, he joined a Baltimore team that was thin at quarterback but still served as a backup on a Super Bowl-winning squad.
Even when Trent Dilfer and Tony Banks departed after the season, Redman remained the backup behind veteran newcomers Elvis Grbac and Randall Cunningham and didn't attempt a single pass in 2001. Redman made six starts in the next two seasons as injuries cut his Ravens career short. He signed with the Pats to be Brady's backup but was waived before the 2005 season.
Falcons coach Bobby Petrino saved Redman's NFL career in 2007 by recruiting his former Louisville QB to be a backup. Redman replaced Joey Harrington as the starter in Week 12 and then made his first starts in five years, playing capably to close the season.
He returned to the bench for the entire 2008 season but filled in for an injured Matt Ryan for a few games in 2009.
Redman played two more seasons in Atlanta but never made another start.
He was released in August of 2012, ending his pro career.
Tee Martin, Steelers, No. 163
Martin was Peyton Manning's backup before leading Tennessee to a perfect season and a national championship in 1998.
Pittsburgh took him in the fifth round, but he never attempted a pass in two seasons there.
He had two games of mop-up duty for Oakland and two seasons in the CFL before becoming a coach, working his way up to a job as USC's offensive coordinator.
That was his last season as a player.
Marc Bulger, Saints, No. 168
Bulger had mixed results at West Virginia and was drafted by New Orleans in the sixth round but was waived in training camp.
He joined the Rams' "Greatest Show on Turf" and got his chance in 2002, when Kurt Warner and backup Jamie Martin went down.
Bulger led the Rams to a 6-0 record before he was hurt, too, but he became the starter the following season when Warner struggled and suffered a concussion in the opener.
He led the Rams to a 12-4 season, went to the Pro Bowl and was MVP of the game while Warner was released.
He took the Rams back to the playoffs in 2004, but he'd go 15-44 over the next five seasons. His play remained elite for a couple more years, however; he topped Warner as the fastest to 1,000 completions in NFL history and became the highest-paid player in Rams history with a $62.5 million deal. But injuries and struggles led the Rams to release him less than three years into his six-year deal.
Bulger spent the entire 2010 season on the bench in Baltimore.
He announced his retirement from football on August 2, 2011
Spergon Wynn, Browns, No. 183
Cleveland has made many mistakes in drafting quarterbacks, and Wynn was another. Coming out of Southwest Texas State after transferring from Minnesota, Wynn played seven games for a 3-13 Browns team in 2000, making one start.
He was traded to the Vikings and made two starts the following season due to injuries to the Vikings' top two QBs. Wynn finished his NFL career with one touchdown pass against seven interceptions and a 39.5 passer rating.
He ended his playing days in 2006 playing in the CFL.