Yadier Molina

Yadier Molina has caught more games for one team than anyone in MLB history. Molina passed Gabby Hartnett by catching his 1,757th game in a Cardinals uniform. The catcher, who will turn 36 next month, is in his 15th season with St. Louis and is signed through 2020. Molina passed another Hall of Famer earlier this year on a different durability-based list, eclipsing Johnny Bench in all-time innings caught. Molina currently ranks 13th on that list.