Other Answers
andre aggassi vs micheal ching facing match point in the third set, aggassi comes from behind to produce "ill never seen a second match point like this again" moment
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The greatest match I ever saw was Andy Roddick vs Elanouyi (sp?) at the Australian Open in 2003. That final set was 21-19. It's a match I could watch again and again when it comes on tv.
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The greatest match ever player was 2007 Wimbledon final between Federer and Nadal. This match had me on pins throughout. Add to this the historic importance for both Fed and Nadal. Fed was shooting for straight 5 wimbys and Nadal was shooting for the first French-Wimby win since Borg. Fed really displayed overall greatness in the 5th set.
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No question it was the 1980 Wimbledon final between John McEnroe and Bjorn Borg. But IMHO that the best match in history is the 1996 Master Cup final between Pete Sampras and Boris Becker. Sampras won 3-6, 7-6, 7-6, 6-7, 6-4.
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Pete Sampras and Andre Agassi in Wimbledon 1994
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Female - Justine Henin vs Venus Williams, semi-final US open, even though Venus went down in straight sets, it was one of the best matches I have ever seen.
Male - Bjorn Borg vs John McEnroe, that would be the match of all time. A 5 set game that will be recognized by every tennis pro for years to come. Bjorg finally taking it after an emotionally and physically straint McEnroe couldn't keep fighting
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Billy Jean King and Bobby Riggs, 1976 Philadelphia