Draft: 1956, 15th-round pick
Team: Cleveland Browns

Davis -- the 181st overall selection out of Grambling State -- was eventually dealt by the Browns to the Green Bay Packers, with whom he was a pivotal performer on five teams that won the NFL championship (including the first two Super Bowls). Davis, who didn't miss a game in his 12-year, 162-game career, was a 1981 inductee into the Pro Football Hall of Fame. (AP Photo/NFL Photos)

Draft: 1960, seventh-round pick
Team: St. Louis Cardinals

Wilson -- the 74th overall selection out of Utah -- is one of the game's all-time great safeties. He is credited with making the safety blitz famous and a vital component of modern defensive football strategy. Wilson was a 1978 inductee into the Pro Football Hall of Fame. (AP Photo/NFL Photos)

Draft: 1953, 27th-round pick
Team: New York Giants

Brown -- the 321st overall selection out of Morgan State -- anchored an offensive line for a Giants team that appeared in six NFL championship games (including one win in 1956). The nine-time Pro Bowl selection was a 1975 inductee into the Pro Football Hall of Fame. (AP Photo)

Draft: 1954, 20th-round pick
Team: Baltimore Colts

Berry -- the 232nd overall selection out of SMU -- formed one of the NFL's all-time great passing combos with Johnny Unitas. Those two helped the Colts win the epic 1958 NFL Championship Game in sudden-death overtime, and then repeat the next season. Berry was a 1973 inductee into the Pro Football Hall of Fame. (AP Photo/NFL Photos)

Draft: 1956, 17th-round pick
Team: Green Bay Packers

Starr, the 200th overall selection out of Alabama, was the field general for all five of Vince Lombardi's NFL title-winning teams in Green Bay. The MVP of the first two Super Bowls, Starr was a 1977 inductee into the Pro Football Hall of Fame. (AP Photo/NFL Photos)

Draft: 1955, ninth-round pick
Team: Pittsburgh Steelers

Unitas -- the 102nd overall selection out of Louisville -- engineered the thrilling conclusion to "The Greatest Game Ever Played." In 1960, Unitas established a record for consecutive games with a touchdown pass that stood for more than 50 years (finally eclipsed by Drew Brees in 2012). Unitas was a 1979 inductee into the Pro Football Hall of Fame. (AP Photo/NFL Photos)

Draft: 1961, 14th-round pick
Team: Los Angeles Rams

Jones -- the 186th overall selection out of Mississippi Vocational College (now Mississippi Valley State) -- became the frontman for the Rams' famed Fearsome Foursome. Jones coined the term "sack" as he terrorized quarterbacks for more than decade. Jones was a 1980 inductee into the Pro Football Hall of Fame. (AP Photo/NFL Photos)

Draft: 1979, third-round pick
Team: San Francisco 49ers

Montana -- the 82nd overall selection out of Notre Dame -- somehow dropped in the 1979 NFL Draft despite enjoying a high level of success with the Fighting Irish, including the 1977 national championship. Montana became a four-time Super Bowl champion with the 49ers, earning three Super Bowl MVP awards in the process. Montana was a 2000 inductee into the Pro Football Hall of Fame. (AP Photo)

Draft: 1964, 10th-round pick
Team: Dallas Cowboys

Staubach -- the 129th overall selection out of Navy -- fell in the draft due to a mandatory four years on active military duty, including service in Vietnam. When Staubach finally got the opportunity to play in the NFL, the result was helping the Cowboys rise to prominence as "America's Team." Staubach led the team to two Super Bowl triumphs, and was a part of five Dallas teams that played on Super Sunday. Staubach was a 1985 inductee into the Pro Football Hall of Fame. (AP Photo)

Draft: 2000, sixth-round pick
Team: New England Patriots

Brady -- the 199th overall pick out of Michigan -- is just the second player representing the draft's modern era (since 1970) on this list (Joe Montana, 1979). Given his eventual unprecedented success, Brady's drop to the sixth round is mind-boggling. It is an omnipresent reminder of how inexact the draft process can still be, despite the significant advances made since the inaugural draft of 1936. Brady's ever-growing Pro Football Hall of Fame resume includes two MVP awards and three Super Bowl wins. (AP Photo/Joe Mahoney)