Diligent searching on YouTube turns up a huge amount of MLB playoff games and various World Series highlights. Here are links to most of the Red Sox's postseason games of the last 40 years.
1946 World Series
Highlights
1967 World Series
Highlights
1975 World Series
Game 1: Red Sox 6, Reds 0
Game 2: Reds 3, Red Sox 2
Game 3: Reds 6, Red Sox 5 (10)
Game 4: Red Sox 5, Reds 4
Game 5: Reds 6, Red Sox 2
Game 6: Red Sox 7, Reds 6 (12)
Game 7: Reds 4, Red Sox 3
1978
AL East Playoff: Yankees 5, Red Sox 4
1986 ALCS
Game 1: Angels 8, Red Sox 1
Game 2: Red Sox 9, Angels 2
Game 3: Angels 5, Red Sox 3
Game 4: Angels 4, Red Sox 3 (11)
Game 5: Red Sox 7, Angels 6 (11)
Game 6: Red Sox 10, Angels 4
Game 7: Red Sox 8, Angels 1
1986 World Series
Game 1: Red Sox 1, Mets 0
Game 2: Red Sox 9, Mets 3
Game 3: Mets 7, Red Sox 1
Game 4: Mets 6, Red Sox 2
Game 5: Red Sox 4, Mets 2
Game 6: Mets 6, Red Sox 5 (10) (2nd copy)
Game 7: Mets 8, Red Sox 5
1988 ALCS
Game 1 (Parts 1 and 2): A's 2, Red Sox 1
Game 2 (Parts 1 and 2): A's 4, Red Sox 3
Game 3 (Parts 1 and 2): A's 10, Red Sox 6
Game 4 (Last Out): A's 4, Red Sox 1
1990 ALCS
Game 1: A's 9, Red Sox 1
Game 4 (Clemens Ejected): A's 3, Red Sox 1
1999 ALDS
Game 3: Red Sox 9, Cleveland 3
Game 5: Red Sox 12, Cleveland 8 (2nd copy)
1999 ALCS
Game 1: Yankees 4, Red Sox 3 (10)
Game 2: Yankees 3, Red Sox 2
Game 3: Red Sox 13, Yankees 1 (2nd copy)
Game 4: Yankees 9, Red Sox 2
Game 5: Yankees 6, Red Sox 1
2003 ALDS
Game 3: Red Sox 3, A's 1 (11)
Game 4: Red Sox 5, A's 4
Game 5: Red Sox 4, A's 3
2003 ALCS
Game 1: Red Sox 5, Yankees 2
Game 2: Yankees 6, Red Sox 2
Game 3: Yankees 4, Red Sox 3 (2nd copy)
Game 4: Red Sox 3, Yankees 2
Game 5: Yankees 4, Red Sox 2
Game 6: Red Sox 9, Yankees 6
Game 7: Yankees 6, Red Sox 5 (11) (2nd copy)
2004 ALDS
Game 1: Red Sox 9, Angels 3
Game 2: Red Sox 8, Angels 3
Game 3: Red Sox 8, Angels 6 (10)
2004 ALCS
Game 1: Yankees 10, Red Sox 7
Game 2: Yankees 3, Red Sox 1
Game 3: Yankees 19, Red Sox 8
Game 4: Red Sox 6, Yankees 4 (12)
Game 5: Red Sox 5, Yankees 4 (14)
Game 6: Red Sox 4, Yankees 2
Game 7: Red Sox 10, Yankees 3
2004 World Series
Game 1: Red Sox 11, Cardinals 9
Game 2: Red Sox 6, Cardinals 2
Game 3: Red Sox 4, Cardinals 1
Game 4: Red Sox 3, Cardinals 0
2007 ALDS
Game 1: Red Sox 4, Angels 0
Game 2: Red Sox 6, Angels 3
Game 3: Red Sox 9, Angels 1
2007 ALCS
Game 1: Red Sox 10, Cleveland 3 (2nd copy)
Game 2: Cleveland 13, Red Sox 6 (11)
Game 7: Red Sox 11, Cleveland 2 (2nd copy)
2007 World Series
Game 1: Red Sox 13, Rockies 1
Game 2: Red Sox 2, Rockies 1
Game 3: Red Sox 10, Rockies 5
Game 4: Red Sox 4, Rockies 3
2008 ALDS
Game 1: Red Sox 4, Angels 1
Game 2: Red Sox 7, Angels 5
Game 3: Angels 5, Red Sox 4 (12)
Game 4: Red Sox 3, Angels 2
2008 ALCS
Game 1: Red Sox 2, Rays 0 (2nd copy)
Game 5: Red Sox 8, Rays 7
Game 6: Red Sox 4, Rays 2
Game 7: Rays 3, Red Sox 1
2013 ALDS
Game 1: Red Sox 12, Rays 2 (2nd copy)
Game 2: Red Sox 7, Rays 4
Game 3: Rays 5, Red Sox 4 (2nd copy) (3rd copy)
Game 4: Red Sox 3, Rays 1 (2nd copy)
2013 ALCS
Game 1: Tigers 1, Red Sox 0
Game 2: Red Sox 6, Tigers 5
Game 3: Red Sox 1, Tigers 0
2013 World Series
Game 1: Red Sox 8, Cardinals 1 (2nd copy)
Game 2: Cardinals 4, Red Sox 2
Game 3: Cardinals 5, Red Sox 4
Game 4: Red Sox 4, Cardinals 2 (2nd copy)
Game 5: Red Sox 3, Cardinals 1
Game 6: Red Sox 6, Cardinals 1 (2nd copy) (3rd copy)
And some random links:
1967
August 19: Red Sox 12, Angels 11
September 30: Red Sox 6, Twins 4
1952 World Series
Game 6: Yankees 3, Dodgers 2
Game 7: Yankees 4, Dodgers 2
20 Strikeouts
April 29, 1986: Roger Clemens vs.