So MLBN has been playing the 20 Greatest Games of the last 50 years. They have reached the top 3 finally.
#20 - Phillies vs Cubs, May 17, 1979 (23-22 win)
#19 - Marlins vs Giants, Gm 4 2003 NLDS (Rodriguez tags Snow)
#18 - Phillies vs Astros, Gm 5 1980 NLCS (10 innings)
#17 - Red Sox vs Yankees, Gm 4 2004 ALCS (12 innings)
#16 - Tigers vs Twins, AL Tiebreaker 2009 (12 innings)
#15 - Yankees vs Mariners, Gm 5 1995 ALDS (M's 11th Inning Win)
#14 - Phillies vs Blue Jays, Gm 6 1993 WS (Joe Carter)
#13 - Indians vs Marlins, Gm 7 1997 WS (Edgar Renteria)
#12 - Diamondbacks vs Yankees, Gm 4 2001 WS (Mr. November)
#11 - Yankees vs Red Sox, AL Tiebreaker 1978 (Bucky Dent)
#10 - A's vs Dodgers, GM 1 1988 WS (Kirk Gibson)
#9 - Yankees vs Diamondbacks, Gm 7 2001 WS (Luis Gonzalez)
#8 - Red Sox vs Angels, Gm 5 1986 ALCS (Red Sox Rally)
#7 - Marlins vs Cubs, Gm 6 2003 NLCS (Bartman)
#6 - Red Sox vs Yankees, Gm 7 2003 ALCS (Aaron Boone)
#5 - Mets vs Astros, Gm 6 1986 NLCS (16 Innings)
#4 - Braves vs Pirates, Gm 7 1992 NLCS (Sid Bream)
#3 -
#2 -
#1 -
Games I think have a chance to be in the top 3 (1961-2011):
At least one of these two will be in the list.
Braves vs Twins, Gm 6 1991 WS (Puckett HR + Catch)
Braves vs Twins, Gm 7 1991 WS (Jack Morris, 10 innings)