Growing up in Texas, Maynard's father was a cotton broker, and with the family constantly moving, Don attended 13 schools, including five high schools. As a senior at Colorado City High School in Colorado City, Texas, he lettered in football, basketball and track.
Maynard played collegiately for Rice University (one year), then for Texas Western College (now the University of Texas at El Paso). In three seasons (1954–56) with the Miners, he caught only 28 passes but averaged an astounding 27.6 yards per reception for 10 touchdowns. As a running back, he had 843 yards rushing on 154 attempts for a 5.4 average and also returned punts and kickoffs. He amassed 2,283 all-purpose yards, while also intercepting 10 passes playing defensive back.
He was selected in the ninth round (109th overall) of the 1957 NFL Draft by the New York Giants. In 12 games as a rookie, he had 12 rushes for 45 yards (3.8 yards per carry), caught five passes for 84 yards (a 16.8 yard average) and played on special teams. However, after being released by the Giants during their 1959 training camp, he played one season in the Canadian Football League with the Hamilton Tiger-Cats, catching just one pass for 10 yards. In the off-season, he worked as a plumber as well as a teacher.
Maynard became the first player to sign with the New York Titans in 1960 (the team was renamed the Jets in 1963). This came about because the Titans' first head coach, Sammy Baugh, had coached against Maynard in college and knew his talent. Although scorned by the New York press as an "NFL reject" in 1960, he teamed with Hall of Famer Art Powell to form the first professional wide receiver tandem to each gain over 1,000 yards on receptions in a season, with the pair achieving this milestone again in 1962. Over the next 13 years Maynard put up receiving numbers that would earn him a spot in the Pro Football Hall of Fame in 1987.
Collecting 72 pass receptions in his first year as a Titan, he went on to compile four more seasons with 50 or more catches and 1,000 yards receiving, and held the professional football record for total receptions and yards receiving. A four-time AFL All-Star, he is sixth in all-time pro football touchdown receptions, and is a member of the All-time All-AFL Team.
In 1965 Maynard was teamed with rookie quarterback Joe Namath. Maynard had 1,218 yards on 68 receptions and 14 touchdowns in Namath's first season (Namath had 22 TD passes that year), and in 1968 the duo hooked up 57 times for 1,297 yards (22.8 yards per catch) and 10 touchdowns (Namath had 15 TD's that year). In 1967, Maynard caught 1,434 of Namath's historic 4,007 passing yards. The receiving yards were a career high for Maynard and led the league; he also had 71 receptions, 10 TD's, and averaged 20.2 yards per catch. In the 1968 AFL Championship Game, a 27-23 Jets victory over the Oakland Raiders, Maynard caught six passes for 118 yards and two touchdowns. His 14-yard catch in the first quarter gave the Jets the lead and his six-yard catch in the fourth quarter proved to be the game winner. The Jets would go on to win Super Bowl III, 16-7 over the NFL's Baltimore Colts, which was hailed as the first "upset" in Super Bowl history. Maynard played, but had no catches while suffering the effects of a hamstring injury in the AFL title game.
One of only 20 players who were in the AFL for its entire 10-year existence, Maynard was also one of only seven players who played their entire AFL careers with one team. Maynard finished his career with 633 receptions for 11,834 yards and 88 touchdowns. His 18.7 yards per catch is the highest for anyone with at least 600 receptions.
Following his NFL career, Maynard went on to participate in many charity-sponsored events. He also participated in the coin toss in Super Bowl XXXIII along with his former teammates, in honor of the 40th anniversary of the 1958 NFL Championship, which is also known as "The Greatest Game Ever Played". He was also once named the grand marshal in the annual El Paso Sun Bowl Thanksgiving Parade. He has worked as a math and industrial arts teacher, sold a variety of products and has been a financial planner, which he still dabbles in.
Maynard currently resides in both El Paso and in Ruidoso, New Mexico to be near his son and daughter and two grandchildren. His son was also a player in the Canadian Football League.
Don and his wife Marilyn (Weaver), whom he met when she was a student at Texas Western, were married in December 1955 after his junior season. Marilyn died several years ago and Don has since remarried.