I thought that Jonathan Schoop would surely have a shot at the games played record, but found this interesting historical quirk.
"When the 1962 season ended the San Francisco Giants and the Dodgers were tied with a 101-61 record. Under the rules of the day, they played a best of three playoff series. The series went all three games, with the Giants winning the pennant. Wills played in all 162 regular season games and the 3 tie-breaker games, which are counted as regular season games, much like today's one-game playoffs are counted as regular season contests.
To date, six players have played 164 games in a season but no one has tied Wills' 165 game mark."