I too, like @GolfLug, remember great wedge, iron shots, or my missed putts, more than my made putts. My most memorable recently, would be:
#17 Old Course St. Andrews (last year)
I had been putting awful all day (I started 3 putt, 4 putt, 3 putt, 3 putt), but found a putting stroke on the back 9 and was 1 under on the back going into 16 and of course I 3-putted it for a bogey. Got to 17 and my playing partner just hit it into the hotel, so I went a little more left and decided to not try and hit it over the hotel. And as soon as my ball was in the air, I heard one of the other caddies do the chicken noise. LOL
My shot was a little more left than I wanted, about 185 yards, I hit a 6-iron and it was drawing right at the flag. The pin was just to the right of he bunker and towards the front of the green. My ball hit short (and just missed going into said bunker) and stopped about 15 feet left of the hole. Had a little left to right break and as soon as I hit it, I knew it was in. Birdie on the road hole, looked at the caddie and said not bad for a Chicken. Parred 18 (missed 10 foot birdie putt) for a 35 on the back 9 at the Old Course.
#18 Springfield G&CC
Last year while playing in our season long match play event, my partner and I get the 18th hole needing to win the match to move on into the knockout round. We are tied going into 18. A tie and we lose on overall points by .5. Our teaching pro is on the other team (very good golfer), so we were pretty sure we needed a birdie to have a chance to win the match, I hit on of the best drives I hit all day and had about 135 yards to the pin, but it was in a place where you didn't really want to be long. So I hit a PW and it landed just short of the flag but released about 12 feet past the hole, so have a devilish putt coming back down the hill. Our competitors were away and the pro missed his birdie putt by inches, I thought it was in when he hit it. So after reading the putt, which probably had a 2 cup left to right break, I made the putt to win the match.
#15 Springfield G&CC
A few years back, was playing in the first round of the Club Championship (against the previous years runner-up) and my putter was balky all day. Got to the 15 hole, 2nd Par 5 on back, and was 3-down with 4 to play. We both hit good drives, both hit good second shots and we both hit decent 3rd shots. I was about 15 feet and he was just a hair longer. He missed his putt, I had another slider putt down the hill, with about a foot of right to left break and made the putt.
I birded the next hole, to go 1 down, but not a memorable putt as I only needed a bogey to beat him on that hole, he had all kinds of issues going on. Lost on 17, as he birdied it, right after I missed mine to lose 2&1.