Phillies:
Mike Schmidt
Richie Ashburn
Steve Carlton
Jimmie Rollins
Braves
Warren Spahn
Henry Aaron
Chipper Jones
One of the big three (Maddox,Smoltz, Galvine)
Bold move, choosing McCovey over one of the top 3 players of all-time 
I love Yogi, one of my favorite players, I’ve even met him and of course visited his museum more than once, but no, Joe DiMaggio, the Yankee Clipper, is one of the 4. He meant more to the Yanks than Yogi and more to Baseball than Yogi. Yogi is a national treasure but Joltin Joe is on another level. I believe Yogi would strongly agree.
Blue Jays:
Dave Stieb
Roy Halladay
Tony Fernandez
Either Carlos Delgado or Jose Bautista… for now, I’ll go with Delgado
Yankees fan, I’d have to break it up in to two… one pre-reserve clause, one post-reserve clause.
Pre-Reserve Clause:
Ruth
Gehrig
Mantle
DiMaggio
Post-Reserve Clause
Munson
Jeter
Rivera
Guidry
Atlanta Braves
Niekro
Aaron
Glavine
Maddux
… With apologies to Dale Murphy, who I edited out when I saw that I forgot Hammerin’ Hank.
Agree, both about the top three (they were the first ones I thought of) and about the fourth being not a universal choice. A case could be made for Albert Pujols, who was with the Cardinals for over a decade and who was considered one of the best players in MLB during that time (he certainly lost some love among St. Louis fans when he left for Los Angeles, but in retrospect that worked out pretty well for the Cardinals); or for Yadier Molina.
Yogi just got it done. He was a winner. Sure, DiMag was a great player, but accounting for his personality, I’d rather have Yogi on my team.
Going to toss out Traynir on my list and add Mazeroski.
Regardless of what anyone else says, no one hit a more impactful HR than Maz in game 7 of the 1960 World Series. The reason it doesn’t get listed as the top HR in baseball history is because a beloved NY team lost… If the Yankees had won that game on a 9th inning HR, it would have supplanted the “shot heard 'round the world.” (NYG Bobby Thompson).
Maz’ swing gave the Pirates their first WS since 1925. He was never the hitter Traynir was (or Arky), but he was arguably the best defensive second baseman ever, and he has one of the most iconic hits in MLB history.
Yep, had to go with Maz. Traynor was awesome, but that image of Mazeroski running into home is one of the most iconic images in pro-sports. My mother remembers watching it with my grandfather when she got home from school. It’s right up there with the Immactulate Reception, as far as Pittsburgh sports go.
You left off Hee Seop Choi! 
Traynor, not Traynir. I swear I know how to spell the man’s name.
I picked McCovey over Mathewson, but I went back and forth on the decision for a while.
Royals:
George Brett (duh)
Frank White
Bret Saberhagen
Alex Gordon
I could easily hear arguments for Willie Wilson, Dan Quisenberry, Kevin Appier and Amos Otis instead of any of those other than Brett.
Here I am racking my brain trying to figure out who mine would be figuring no Brewer would be listed…and it’s in the second post!
My only question is since Young and Molitor were basically the same year, and this is supposed to be generational, replace one with Hank? (aaron, not the dog)
Hank, Yount, Fielder (screw Braun I miss Prince), Uecker
I like that you put Youk, that was a smart thing
For the Twins:
Killebrew
Puckett
Carew
Mauer
Mauer edged Oliva and Blyleven, but it was close. I refuse to accept Walter Johnson as a Twin.
I’m not sure I would agree with a list that includes only one person who substantially helped the team win one of its two World Series.
I’d replace Delgado/Bautista with Roberto Alomar, for sure. Alomar was as great a player as either of those guys and was the best overall player on two World Champions, which is saying a hell of a lot. He is in the Hall of Fame, as deserves to be, and 1992-1993 was the apex of his career.
It’s hard to argue with Stieb or Halladay just because they were so great - Stieb is one of the most underrated players of modern baseball - and Fernandez is an easy choice. Toronto has no lifetime superplayers like Tony Gwynn or Carl Yastrzemski, so you can argue for or against like fifteen guys.
Jose Bautista is an incredible player but I’d be unwilling to carve him into the mountain when the book isn’t closed on him yet. If Toronto makes the playoffs this year and wins something, then his argument becomes way stronger. If they don’t, he’ll be gone from Toronto in 2016 with no playoff games to his credit. and at that point it would be very hard to figure out who to dump to make room for him. I’d be inclined to lose Delgado.
Yaz’s period of “impactfulness”, at least at Rushmore level, was pretty brief, arguably only one glorious season. Pedro was as dominant an October performer as there ever was for an extended period. So he gets my vote.
David Ortiz has been, if anything, even more “impactful” as a community leader than a hitter, and I’d tie him with Ted for #1 on my list (Note that, after the Marathon bombings, the community didn’t look to the mayor or governor or cardinal etc. to say the right thing, we looked to the designated hitter. And he came through, too).
I could entertain arguments for Babe Ruth, Smokey Joe Wood, and Johnny Pesky, too.
Man, you’re selling Yaz way short. He was the best player in the American League for five or six years. The 60s made people’s numbers look flat but Yaz had three or four years, at least, better than any David Ortiz season. His 1968 looks ordinary by modern standards, but he was better than Miguel Cabrera was when Cabrera won the Triple Crown. (It helps Yaz was a tremendous glove man.)
Admittedly Yaz never won a World Series but he dragged the Red Sox to a pennant, in the days you had to win the entire league to say that, to an extent hardly any Hall of Famer can say.