Not necessarily the best, just the ones that I suspect are most widely known among people who are at least casual fans. Sometimes what they really remember (or know of, if before their birth) is the moment (rather than knowing the year or even the teams) but I still count that.
UPDATED May 7, reordered a bit.
1. Game 4, 2004 ALCS (really what people know about is Games 4-7)
2. Game 7, 2001 World Series (I'm surprised I hadn't thought of this first, but if it didn't even cross my mind then who else's mind isn't it crossing? - Yankee fans of course will fondly remember the back-to-back heroics in Games 4-5)
3. Game 6, 2003 NLCS (Bartman's foul ball)
4. Game 6, 1986 World Series (you could argue for this higher depending on the average age of these hypothetical casual fans - a lot here hinges on how old you think these fans are and how Northeastern they are)
5. Game 1, 1988 World Series (Kirk Gibson's home run vs. Dennis Eckersley)
6. 1951 NL tie-breaker ("the shot heard round the world")
7. Game 5, 1956 World Series (Don Larson's perfect game)
8. Game 6, 1975 World Series
9. April 1974: Hank Aaron breaks Babe Ruth's record
10t. Game 7, 1992 NLCS (usually framed as an attack on Barry Bonds for not throwing Bream out)
10t. 1978 AL tie-braker (the Bucky Dent game)
Removed from the list above: Texas 30, Baltimore 3 (formerly #7 hence Paul's comment), Ruth's called shot, Pujols HR vs. Lidge, Game 7, 1960 World Series (Bill Mazeroski's home run)
Would you consider Game 2, 2000 World Series? ("Clemens throws bat head at Piazza," but I don't think people associate this with a specific game.) It probably wouldn't make the top 10 anyway, would it?
And I don't think people especially remember the games in which career records were broken (McGwire #62, Bonds #71, Bonds #756, Rickey's stolen base -- for a quick 10 points each name the opponents in any of those games) so much as that they were broken.
Another honorable mention: Game 1, 1996 ALCS (Jeffrey Maier)
Meanwhile, the game that inspired this post was Game 5, 1999 NLCS (Mets over Braves in 15), yet I don't think even that game makes the top ten. (Trying to pretend to be a casual fan, I'd slot it ahead of Jeffrey Maier but behind Sid Bream. Game 7, 1992 NLCS should probably replace Ruth's called shot in the 10 proper, since it's not like people can readily place the year or opponent on that, just the idea that Ruth did it once.)
Last honorable mention before I finally let this post lie: Game 5, 1995 ALDS. If ever there was a game that I thought would resonate through the ages, and that arguably ought to... and yet I claim that hardly anyone ever even thinks of this game.
Posted by Matt Bruce at May 6, 2008 12:08 PMMatt--
Game 7, 2001 Series, is the game vividest in my memory of any I've seen on TV in my lifetime. Post-9/11 NY drama, game 7 drama, Johnson comes in from the bullpen, Rivera officially stops being the Unhittable Man, various in-game moments of high emotion and suspense...
I think maybe we have different ideas of how distinct the categories "memorable game" and "memorable moment" are.
--Nate
Posted by: Nate at May 6, 2008 03:12 PM#7 doesn't belong on this list. It's a curiosity, but I don't think anyone really remembers it. The Shot Heard Round the World belongs in its place. Actually, it belongs higher.
Posted by: Paul at May 6, 2008 03:52 PMNobody remembers the 30-3 game except Rangers fans, Orioles fans and Nats fans who hate the Orioles.
Memorable Orioles game - September 5, 1995 (http://www.baseball-reference.com/boxes/BAL/BAL199509050.shtml) - Ripken breaks Gehrig's record.
Also memorable games for current baseball fans:
Game 6, 1993 World Series (Joe Carter's walk-off homer)
April 8, 1974 (http://www.baseball-reference.com/boxes/ATL/ATL197404080.shtml) Aaron breaks Babe Ruth's record.
The Sox-Yankees playoff in 1978? Maybe it's the New Englander in me, and on top of that one who just read a whole book about it, but that's strikes me as an obvious omission.
Posted by: Cooch at May 7, 2008 08:33 AMAnd now that I read further down, it's killing me I can't remember who the stolen base was against ... the Rangers?
People might remember McGwire's because of the ties with Sosa. Other than that, point taken.
Posted by: Cooch at May 7, 2008 08:37 AM