Among the games I've attended in person, here are a few from 1979 to 2007 (road team listed first):
9/16/79: Tigers/Yankees, second-ever MLB game (the first was an Expos/Phillies game on 8/7/79) - I don't really remember the game (the Tigers won 8-4 in 12 innings), but what was notable is shown in the box score, particularly Yankee closer Goose Gossage's pitching line.
http://www.retrosheet.org/boxesetc/1...160NYA1979.htm
10/1/81: Cardinals/Phillies - my father won tickets for this game, which was played the last week of the strike-stricken, 1981 season. During this season MLB made the decision to split the season into halves, and award split season division championships to the teams who had the best records before the strike and after the strike. The Cardinals were in contention for the 2nd half division title, so this game needed to be completed. That became problematic considering it was a Thursday night, the game went into a rain delay in the 8th inning, and the game was tied. My father and I stuck around for a little while, getting to see a guy who ran onto the field and was sliding around on the Astroturf in the outfield before getting caught by security. After that diversion, my dad suggested we leave because I had school the next day and we lived a minimum of 1 1/2 hours away. We went home, and I went to bed when we returned. Meanwhile, my father turned on the TV just as the game was coming out of the rain delay and watched on TV the remainder of the game we attended 70 miles away. The Cardinals scored a run in the 10th inning to win 3-2, though ultimately they fell short of winning the NL East 2nd half title. (The Expos won that crown and defeated the Phillies in the first NLDS before falling to the Dodgers in an excellent NLCS.)
Retrosheet Boxscore: St. Louis Cardinals 3, Philadelphia Phillies 2
5/25/01: Expos/Phillies - the Phillies' Travis Lee hit a long, line drive, 3-run, game-winning home run with 2 outs in the bottom of the 9th and the Phillies behind by 2 runs to cap a late Phillies comeback and give them a 10-8 win.
http://www.retrosheet.org/boxesetc/2...250PHI2001.htm
7/8/01: Phillies/Orioles - Travis Lee hit
another 3-run home run in the 9th inning with the Phillies trailing by 2 runs to give the Phillies a come-from-behind 5-4 victory over the Orioles.
http://www.retrosheet.org/boxesetc/2...080BAL2001.htm
9/21/01: Yankees/Orioles - this was the first Yankees (and Orioles) game played after the 9/11 attacks, and one heck of a game. The Orioles led 5-3 going into the 9th inning, but the Yankees scored 3 runs in the top of the 9th to take a 6-5 lead. However, the Orioles didn't fold and responded with 2 runs in the bottom of the frame off of Mariano Rivera to post a 7-6, walk-off victory.
http://www.retrosheet.org/boxesetc/2...210BAL2001.htm
5/6/03: Tigers/Orioles - the Tigers' Dmitri Young had a career game, going 5 for 5 with 2 home runs, 2 triples, and a single. He was the first player with 2 homers and 2 triples in the same game since Willie Mays in 1958. Each of his hits drove in a run. His last hit in the top of the 9th inning was a deep fly ball off the CF wall that was about 3 feet from being his third home run of the game (and his first batting right-handed; his 2 homers both occurred when he hit left-handed). He could have stopped at 2nd base to complete the cycle but instead went to 3rd for his second triple. Oh, and that hit broke a 6-6 tie and eventually gave Detroit (who finished 43-119 that year) a 7-6 win. Young's heroics weren't the only notable plays in the game; the Tigers' Shane Halter also hit an inside-the-park home run during the game. Amazingly, this was not the most memorable game I've seen that included an inside-the-park home run as a side note (more on that in a future post).
http://www.retrosheet.org/boxesetc/2...060BAL2003.htm
6/21/03: Red Sox/Phillies - the Phillies won 6-5 in 13 innings in a truly remarkable game. The game was tied at 2-2 entering extra innings. Boston scratched out a run in the 12th to take a 3-2 lead, but Jim Thome hit a game-tying home run to continue the game. In the 13th, the Red Sox scored a pair of runs to take a 5-3 lead. However, the Phillies responded again, and Todd Pratt hit a walk-off 2-run homer to give the home team a 6-5 victory. Nomar Garciaparra went 6-6 in the game at the plate.
http://www.retrosheet.org/boxesetc/2...210PHI2003.htm
7/6/03: Blue Jays/Orioles - the Orioles appeared to have this game won, taking a 3-1 lead in the 9th inning. However, the Blue Jays scored a pair of runs to force extra innings, and tallied 2 more runs in the 10th inning to stun Baltimore 5-3. The Orioles wasted a strong pitching performance by Rodrigo Lopez.
http://www.retrosheet.org/boxesetc/2...060BAL2003.htm
5/23/04: Rockies/Mets - this game is the closest I've come to seeing a MLB perfect game and second-closest to seeing a MLB no-hitter. (I did see a 9 inning, minor league no-hitter by current A's pitcher Tyler Clippard in 2006 when he was pitching for Trenton against Harrisburg in Double A.) Tom Glavine had a perfecto until the first batter in the 7th when he walked a Rockies player, but maintained his no-hitter until 2 outs in the 8th when the Rockies posted their only hit of the game, a double off the RF wall. Glavine did manage to pitch a complete game, 1-hit shutout, and the Mets beat Colorado 4-0.
http://www.retrosheet.org/boxesetc/2...230NYN2004.htm
7/22/05: Padres/Phillies - Chase Utley hit a no doubt about it 2-run, game-winning home run in the 11th inning to give the Phils an 8-6 win. This game was also the middle game of games I attended in Washington, Philadelphia, and Cleveland on 3 consecutive days; the other two games were one-run, 9 inning games.
http://www.retrosheet.org/boxesetc/2...220PHI2005.htm
9/3/06: Braves/Phillies (Game 1) - Ryan Howard hit home runs in his first 3 at-bats and the Phillies came back from a 7-6 deficit in the bottom of the 9th to win 8-7. The Phillies led 7-1 through 7 innings and 7-3 through 8 innings, but Atlanta scored 4 runs in the top of the 9th to take the lead. This game is the only MLB (or probably professional) game where I've seen a player hit 3 home runs in a game. The Braves won the second game 3-1 in 11 innings.
http://www.retrosheet.org/boxesetc/2...031PHI2006.htm
9/16/06: Rockies/Diamondbacks - I was visiting my brother in the Phoenix area, having arrived the day before, and I was a little jet-lagged. This game didn't help. The Rockies scored 2 runs in the top of the 9th to tie the game 6-6 and force extra innings. Neither team was able to score until the 16th inning, when the D-Backs managed to score a run to win 7-6. This 16 inning affair is the longest MLB game I've ever attended by innings played. (I also saw a 16 inning game in the minors in 2004.) Making things worse is I wanted to get up early the next morning to go to the sports bar for the 10 AM kickoff of the Giants/Eagles game, a game that the Eagles blew late due to a bad penalty by Trent Cole.
http://www.retrosheet.org/boxesetc/2...160ARI2006.htm
9/28/06: Orioles/Yankees - the wildly inconsistent Daniel Cabrera had one of the best pitching performances of his life, pitching a no-hitter for 8 1/3 innings as the Orioles won 7-1. The Yankees actually scored a run without the benefit of a hit in the 7th inning on 2 Orioles errors and 2 passed balls (all of which were called correctly IMO). Baltimore committed 3 errors in all; only the first of the errors was questionable (though I thought it was the right call). The Yankees managed a single in the 9th to break up the no-no bid. This game featured the deepest no-hit bid of any MLB game I've seen in person. (See 5/23/04 game listing for additional comments.)
http://www.retrosheet.org/boxesetc/2...280NYA2006.htm
4/27/07: Marlins/Phillies - the Phillies ended up winning this back-and-forth affair 6-5 in the bottom of the 9th. The Phils trailed 5-4 going into the bottom of the 8th but scored a pair of runs to take the lead. However, the Marlins scored a run in the top of the 9th to tie the game, but the Phillies responded, scoring a run in the bottom of the frame to walk off with the victory.
http://www.retrosheet.org/boxesetc/2...270PHI2007.htm
6/23/07: Indians/Nationals - the Indians trailed 3-1 going into the 9th inning but scored 3 runs against Nationals closer Chad Cordero to post a 4-3, come-from-behind win.
http://www.retrosheet.org/boxesetc/2...230WAS2007.htm
6/29/07: Angels/Orioles - this see-saw game saw the Angels jump out to a 5-0 lead through 1 1/2 innings. The Orioles responded by scoring 7 runs over 4 innings to take a 7-5 advantage through 5 innings. However, Anaheim scored single runs in the 7th and 8th to tie the game, and 2 more runs in the 9th to win 9-7. In the midst of all this scoring, the Orioles' Aubrey Huff hit for the cycle; it is the only cycle I've ever seen in person at a MLB game.
http://www.retrosheet.org/boxesetc/2...290BAL2007.htm
7/22/07: Phillies/Padres - this game featured a pitching mismatch of epic proportions, with the Padres starting eventual 2007 NL Cy Young Award winner Jake Peavy and the Phillies countering with the not-quite immortal J.D. Durbin, who ended up pitching 72 2/3 innings in his MLB
career. My brother and I also attended the game the night before (a Phillies 12-4 victory on a night the Padres honored Tony Gwynn's induction into the Hall of Fame), so I was happy the Phillies would at least split the two games we attended in San Diego. The game ended up being a pitching mismatch alright - the Phillies knocked around Peavy for 4 runs in 6 innings (and then 5 more runs against Padres relievers) while Durbin pitched the game of his life, finishing with a 5 hit, complete game shutout as the Phils blanked San Diego 9-0.
http://www.retrosheet.org/boxesetc/2...220SDN2007.htm
7/26/07: Marlins/Diamondbacks (ARI 7, FLA 4)
7/27/07: Braves/Diamondbacks (ARI 8, ATL 7)
7/28/07: Braves/Diamondbacks (ARI 4, ATL 3) - the Diamondbacks won 3 consecutive games on 3 consecutive days in their last at-bat. In the 7/26 game, Eric Byrnes hit a 3-run homer in the 9th to give Arizona the win. In the 7/27 game, Tony Clark hit a solo homer in the 11th to give the D-Backs the victory. Finally, in the 7/28 game, Arizona scratched a run in the 10th to post another extra inning win. The Diamondbacks also won games I attended on 7/23 and 7/24. Despite the 5 wins however, they were still outscored in the 6 games I attended that week; the Braves demolished the D-Backs 14-0 on 7/29.
http://www.retrosheet.org/boxesetc/2...260ARI2007.htm
http://www.retrosheet.org/boxesetc/2...270ARI2007.htm
http://www.retrosheet.org/boxesetc/2...280ARI2007.htm
8/15/07: Orioles/Yankees - at this weekday matinee at Yankee Stadium II (1976-2008 stadium), the Orioles appeared to be cruising to victory, taking a 3-0 lead into the bottom of the 9th. However, the Yankees struck for 3 runs to tie the game and force extra innings. The Orioles responded however, scoring 3 runs of their own off of Mariano Rivera in the top of the 10th inning to post a 6-3 win.
http://www.retrosheet.org/boxesetc/2...150NYA2007.htm
9/30/07: Nationals/Phillies - the Phillies jumped out to a 3-0 lead over the Nationals after 3 innings, and eventually cruised their way to a 6-1 victory. Combined with the Mets' 8-1 loss the same day to Florida (a game in which the Marlins scored 7 runs in the top of the 1st inning), the Phillies were able to clinch the NL East title and their first playoff appearance in 14 years. There was a lot of celebrating in the ballpark and the parking lots by most fans after that game.
http://www.retrosheet.org/boxesetc/2...300PHI2007.htm
In addition to the above, a couple of minor league games deserve mention. The first was alluded to above; on 8/17/06 I saw Tyler Clippard pitch a 9 inning, complete game no-hitter for Trenton (Yankees affiliate) to give the Thunder a 9-0 win over host Harrisburg (Nationals affiliate). The second occurred on 5/23/07 also in Harrisburg; after scoring 3 runs in the top of the 9th inning, Erie (Tigers affiliate) took a 7-0 lead into the bottom of the 9th. However, Harrisburg made a miraculous comeback, scoring 7 runs in the frame, including 5 with 2 outs, to tie the game. The Senators then completed their comeback by scoring a run in the bottom of the 10th to somehow post an 8-7 win.
I'll list my most memorable MLB games from more recent seasons in a follow up post (or posts).