Hall of Fame: Yes
Career highlights: Rookie of the year in 1972. His home run in Game 6 of the 1975 World Series was not only dramatic, it changed the way sports are televised (NBC lucked into the reaction shot of him waving the ball fair). Eleven All-Star teams, one Gold Glove, high of third in MVP voting (1983). Led league in triples in 1972.
Slash line: .269/.341/.457
Games caught after age 30 season: 1290. Age in last season as regular catcher: 43. Win shares from age 30 on: 240. Win shares after age 33: 173
How long did Carlton Fisk's career extend? The man hit 37 homers (his career high) at age 37. He also stole 17 bases that season. He made his major league debut at age 21, and left the field at age 45, having set the record for games caught (since broken by Ivan Rodriguez).
Paradoxically, I believe that one reason for Fisk's longevity was injuries. He played in just 52 games in 1974, 79 games in '75 — the result of a horrific knee injury that could have ended his career early. While the injury took away the equivalent of a full season from him, it probably helped in the long run by giving him an extended break from the daily grind of squat-and-rise that does incremental, long-term damage to the back, hamstring and knees.
Whatever the cause, Fisk is the one most obvious outlier, the catcher who maintained his level of performance literally for decades.