I have to give Baseball Almanac credit for this one, but I thought I'd reprint this list since it's completely in the spirit of Baseball Junk Drawer.
Have you ever wondered who was the last active Brooklyn Dodger or the last active St. Louis Brown? It's right here, but I thought I'd go a step farther than B-A's list and add the defunct Milwaukee Brewers (precursors of the Browns) and Baltimore Orioles (precursors of the Yankees). Someday I'll probably be adding the last Montreal Expo as well.
What a list! Five Hall of Famers show up, as does another who some people think belongs but I personally don't (Jim Kaat). Kaat holds the record for outlasting his pre-shift franchise by the most seasons, 23. Vic Power outlasted his franchise by the fewest seasons, with only 11. It should also be noted that Mathews and Mays both played in the World Series during their final seasons, so those dates for their final games only reflect the regular season.