Since 1976, the last player selected in the NFL draft has been dubbed Mr. Irrelevant and invited to a celebration called Irrelevant Week. The event, which was founded by former NFL player Paul Salata, raises money for Orange County charities. You can read about the this year's Mr. Irrelevant at theundefeated.org.
The Vintage Football Card Gallery has pictures of cards only up to 1979, so it includes only one card of an official Mr. Irrelevant. It also, however, includes cards of some players who would have been named Mr. Irrelevant if the title had been awarded earlier. Most of these players turned out to be relevant, after all, or they would not have made it onto football cards. Following are all of players in the Gallery who were chosen last in the NFL draft. For a full list of the players who were drafted last, see Wikipedia's article on Mr. Irrelevant.
Bill Fischer, 1948
Bill Fischer was the final player chosen in the 1948 draft; the Chicago Cardinals picked him in the 32nd round. Fischer stayed at Notre Dame in 1948, however. The Cardinals persisted and drafted him again in 1949, this time in the first round. Fischer played five seasons for the Cardinals and went to three Pro Bowls.
Fischer is shown here on his rookie card, a 1948 Leaf, still with Notre Dame. He also appeared on several other Leaf and Bowman cards.
John Schweder, 1949
John "Bull" Schweder was the 251st and last player chosen in the 1949 draft. The Philadelphia Eagles picked him, but he apparently did not make their roster in 1949. In 1950 he joined the Baltimore Colts, but the Colts folded after the season, and the team's players were made available in the 1951 draft. In 1951, Schweder was again drafted, this time at pick number 103, by the Pittsburgh Steelers. He played for the Steelers from 1951 to 1955.
Pictured here is one of Schweder's rookie cards, a 1952 Bowman Small. He also appeared on several other 1950s Bowman cards.
Sisto Averno, 1951
Sisto Averno was another member of the 1950 Baltimore Colts team who ended up in the draft when the team disbanded. Averno was the last player chosen in 1951, by the Cleveland Browns in the 30th round. He played for the New York Yanks in 1951, and the Yanks folded at the end of that season. The NFL gave the remnants of the Yanks to a new franchise in Dallas in 1952, and--guess what?--that franchise also folded at the end of the season. In 1953, the league awarded the remains of the Dallas team to another Baltimore Colts franchise, and Averno spent two years with the new Baltimore team before calling it a career. (See Bob Carroll's article at profootballresearchers.com for a detailed description of the churn in the NFL in the early 1950s.)
Averno appeared on one card, the 1953 Bowman pictured here.
Jacque MacKinnon, 1961
Jacque MacKinnon was the last player chosen in the 1961 NFL draft. The Philadelphia Eagles chose him with the 280th overall pick. He instead went to the AFL's San Diego Chargers, and in nine years with the Chargers, he made the Pro Bowl twice.
The card pictured here is MacKinnon's rookie card, a short print in the 1964 Topps set. He also appeared on several other Topps cards in the late 1960s. (On his 1969 Topps card, he looks like Emilio Estevez!)
Mike Snodgrass, 1962
Western Michigan's Mike Snodgrass was the last player chosen in the 1962 NFL draft. The Green Bay Packers chose him with the 280th overall pick. Snodgrass never played for the Packers, but he did play for the CFL's Ottawa Rough Riders in 1962. He appeared on this Post Cereal CFL football card in 1963.
Stan Hegener, 1975
Stan Hegener was the last player chosen in the 1975 NFL draft. The Pittsburgh Steelers chose him with the 442nd overall pick, but he apparently did not make the team. The card pictured here is a 1973 Nebraska playing card, from his college days. He also appeared on a 1974 Nebraska playing card.
Jim Kelleher, 1977
Jim Kelleher is the only official Mr. Irrelevant in the Gallery. The Mr. Irrelevant title was first awarded in 1976, and Kelleher was the last player chosen in the 1977 NFL draft. The Minnesota Vikings chose Kelleher with the 335th overall pick, but he did not see playing time in the NFL. The card here pictures Kelleher on his 1974 University of Colorado playing card.