[BostonCard]

Mays: 3005 games played, but his career included 135 games with the Mets at the end of his career, so only 2870 with the Giants.
Cobb: 3034 games played, but he spent two seasons with the Philadelphia Athletics at the end of his career (228 games), so he only played 2806 with Detroit
Aaron: 3298 games, but only 1270 were with the Atlanta Braves, so the source I had didn't count his games with the Milwaukee Braves.  If you do include them, then he gets to 3076 games, and so should be counted (and there would be a fourth player).

A hint for the top three (most games with a single franchise):
All-time leader was a member of the Red Sox.
The number 2 (if you exclude Aaron) was a Cardinal
One player just barely qualifies, with 3001 games for the Orioles.

BC

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A few others of note...

Pete Rose has the career record for most MLB games played, but only 2722 were with the Reds.
The top Yankee was Derek Jeter, with 2747 games
The top Giant is Mayes if you include New York Giants games (2730 total as a Giant, of which 2095 were as a San Francisco Giant), but if you look at San Francisco Giants only, it's Willie McCovey (2256)
Considering that it is a relatively young Franchise, the top Padre, Tony Gwynn, played a lot of games (2440), more than, for example the top two Pirates, who were Roberto Clemente and Honus Wagner, who tied for the most games played as a Pirate (2433)
Given how old the franchise is, it's kind of crazy that the career games leader for the Cleveland Indians/Guardians was Terry Turner, who played 1619 in the dead ball era.
Ricky Henderson played the most games for the Oakland A's (1704), if you include KC and Philly, then Bert Campaneris had 1795

BC

[BostonCard]

Mays: 3005 games played, but his career included 135 games with the Mets at the end of his career, so only 2870 with the Giants.
Cobb: 3034 games played, but he spent two seasons with the Philadelphia Athletics at the end of his career (228 games), so he only played 2806 with Detroit
Aaron: 3298 games, but only 1270 were with the Atlanta Braves, so the source I had didn't count his games with the Milwaukee Braves.  If you do include them, then he gets to 3076 games, and so should be counted (and there would be a fourth player).

A hint for the top three (most games with a single franchise):
All-time leader was a member of the Red Sox.
The number 2 (if you exclude Aaron) was a Cardinal
One player just barely qualifies, with 3001 games for the Orioles.

BC

---

A few others of note...

Pete Rose has the career record for most MLB games played, but only 2722 were with the Reds.
The top Yankee was Derek Jeter, with 2747 games
The top Giant is Mayes if you include New York Giants games (2730 total as a Giant, of which 2095 were as a San Francisco Giant), but if you look at San Francisco Giants only, it's Willie McCovey (2256)
Considering that it is a relatively young Franchise, the top Padre, Tony Gwynn, played a lot of games (2440), more than, for example the top two Pirates, who were Roberto Clemente and Honus Wagner, who tied for the most games played as a Pirate (2433)
Given how old the franchise is, it's kind of crazy that the career games leader for the Cleveland Indians/Guardians was Terry Turner, who played 1619 in the dead ball era.
Ricky Henderson played the most games for the Oakland A's (1704), if you include KC and Philly, then Bert Campaneris had 1795

BC