On the men's side:
1981 Masters final - Gerulaitis led Lendl by 2 sets to love and had a match point in the 3rd set tiebreak (Lendl saved it with some excellent play but he could have played it more aggressively) - that would have been the biggest title of his career and in his home city. While he could have beaten Borg in their 1977 Wimbledon SF classic (he had a game point to go 3-1 ahead in the 5th set though still no guarantee that he holds on), and IMO should have beaten McEnroe in their 1981 US Open SF (but failed to convert any of the 9 break points he had in the 5th set), it's difficult to picture him going on to win either final (especially vs. Borg at the 1981 US Open).
Either of Clerc's semi-finals at RG in 1981 or 1982 - In 1981 he had a match point vs. Lendl in the 4th set tiebreak (though Lendl saved it with an unreturnable serve), who he beat in their other 3 matches on clay that year. In 1982 he was 5-1 down in the 4th set and levelled it at 5-5, before his momentum collapsed as he hit 4 straight UEs in the next game (before Wilander's sportsmanship to insist that a match point that went his favour due to a contested line call was replayed). He would have no chance of beating Borg in the 1981 final, and would have been the underdog vs. Vilas in the 1982 final, but regardless it would have been nice to have seen him in the final of a major.
Lapentti's 2002 Wimbledon QF vs. Nalbandian - Lapentti came from 2 sets to love down to force a decider, though he was always trailing in that 5th set going down a double break before clawing one of them back. He saved 4 match points in his R1 match vs. Jamie Delgado, came from 2 sets to love down to win his R3 match vs. Pavel in R3, and from 2 sets to 1 down to win his R4 match vs. Clement. Had he got past Nalbandian I'm not sure how much he would have had left in the tank for a SF against Malisse, but still I would have loved to have seen his Wimbledon adventure continue for longer.
El Aynaoui's 2003 Australian Open QF vs. Roddick when he had match point when leading 5-4 in the 5th set (though on Roddick's serve with he saved with an inside out forehand cross court winner) narrowly misses the cut. I find it difficult to suggest big matches where the player I supported was convincingly beaten, i.e. Gerulaitis in the 1979 US Open or 1980 RG finals, Mecir in the 1986 US Open and 1989 Australian Open finals, Mancini in his 1989 RG QF, Mantilla in the 1997 Hamburg final, Lapentti in his 1999 Australian Open SF, Arazi in the 2001 Monte-Carlo final, Calleri in the 2003 Hamburg final etc.