I'm probably older than most of you here, so I'd been to a lot of games long before the Rockies existed. So forgive me, a lot of these are from Cincinnati or St. Louis. In all these games, I remembered the big events, but to confirm my memories and get the dates, I looked up the details on bb-ref.
July 19, 1965: My first major league game, 10 years old, Crosley Field, Pirates vs. Reds. Tommy Harper led off the game for Cincy in the bottom of the 1st with a HR, but the Pirates won 3-1. Vern Law beat Joe Nuxhall. In the lineups were Pete Rose, Tony Perez, Frank Robinson, Roberto Clemente, Bill Mazeroski, and Willie Stargell. Time of game 2:18, brisk but not all that unusual at the time. Before the game I saw Rose standing at the railing talking to some fans. My parents, bless them, encouraged terrified little kid me to go ask him for his autograph on a scorecard. Pete was in his 3rd season at the time, the first (of 15!) in which he would hit .300. I still have that scorecard.
June 9, 1968: Crosley Field, Sunday afternoon doubleheader, Reds vs. Cardinals. Cards were WS champs, and on their way to another pennant, their 3rd in 5 years, and a 7-game WS loss. In Game 1, the Reds led 8-0, then the Cards scored 10 runs in the 5th and won 10-8. In Game 2, the Cards scored 5 in the 1st, but the Reds fought back and won 7-6 in 12 innings on a Leo Cardenas double that scored Tony Perez from 1b, off a young Cardinal reliever named Steve Carlton. (Who had started game 1 many hours earlier - they sure handled pitchers differently back then!)
July 13, 1973: Jack Billingham for the Reds vs. the great Met HOFer Tom Seaver. Billingham wins, 2-1, in an amazing pitchers' duel that was completed in a tidy 1 hour and 37 minutes. That day was the closest I ever came to seeing Willie Mays play -- he was on the Mets' roster but didn't play in either game of that day's doubleheader. Also, when I pointed out Mets manager Yogi Berra to my companion, who wasn't much of a fan, she was astounded to learn that he was a real person.
Sept. 14, 1973: Braves at Reds, Riverfront. Reds walkoff with 3 in the 9th, Phil Gagliano drove in the tying run. Then Bobby Tolan, who had looked like a young superstar before losing an entire season to injury after tearing his Achilles in an offseason basketball game and who was nearing the end of a miserable (.206/.251/.304) year, his last with the Reds, drove in the winner.
April 7, 1975: Dodgers at Reds, Opening Day, my only Cincy opener - my only opener period, come to think of it, but in Cincy it's pretty much a civic holiday. My girlfriend (who had scored the tickets for me as a birthday gift) and I cut classes at Ohio State and drove down from Columbus. Our seats were actually in the football pressbox down the RF line at Riverfront. It was warm if you were in the sun, but freezing in that shaded concrete box. The Reds beat the Dodgers 2-1 in 14 innings, and went on to win 108 games and first WS since 1940.
Not exactly great games, but in my time in St. Louis in the late 70s/early 80s I was present for two very memorable events - Bob Gibson's sad final career game in Sept. 1975, when he gave up a grand slam to the last batter he faced, Pete LaCock; and the 1981 game where Garry Templeton had his famous meltdown and gave a "special greeting" to the fans behind the first base dugout, including me.
Also in St. Louis was the closest I ever came to seeing a no-hitter, albeit what would have been a combined one, was May 12, 1977, when Ken Griffey (Sr.) doubled to the opposite field with 2 out in the 8th for the Reds' only hit of the game.
Since moving to Colorado in 1998, three games really stand out in my memory:
June 20, 2002: Rox fall behind 7-1 to the Yankees, score 8 in the 6th to take a 10-8 lead, Yanks tie it with 2 in the 9th, the Todd Zeile hits a 3-run HR in the 10th for a 14-11 win.
July 8, 2006: Vs. Arizona, game is tied 1-1 going to the 9th, Arizona scores 7 in the top of the 9th, Rockies come back with 6 in the bottom half but Omar Q. strikes out with 2 runners on to end it, as the Rox lose 8-7.
July 6, 2010: Rox score 9 in the 9th to beat the Cardinals 12-9, on a Seth Smith walkoff HR.