One of them, though, was the most significant of his long and distinguished career.
A perfect game is hard to top, but a victory in relief during his baseball twilight was the milestone that really set Martinez apart and made "El Presidente" even more of a hero in his homeland.
On Aug. 9, 1998, the right-hander from Nicaragua won his 244th and next-to-last game. With it, he became the winningest Latin American pitcher in Major League history.
Hall of Famer Juan Marichal held the record previously, and 243 had become a magical number in Latin America, just like 61 homers was in the United States until Mark McGwire flew by it that same year en route to 70.
Martinez had tied Marichal on June 2 with a stunning shutout at Milwaukee. Sent to the bullpen soon afterwards, it was more than two months later before he broke the record, and it happened in San Francisco -- where Marichal had baffled hitters for the Giants.
Martinez, the first player from his country to make the Majors, tossed a perfect eighth inning for the Braves and was the pitcher of record when Chipper Jones broke a tie with a two-out, two-run single in the ninth inning.
"It hasn't been easy, but I guess everything comes in its time," Martinez told reporters afterwards. "I knew it would happen sooner or later, but I never expected it to happen in the place where the man used to pitch."
"I wish he had gone somewhere else and won the game," Giants outfielder Marvin Benard, the only other Nicaraguan in the Major Leagues, told reporters. "But I'm happy for him. I'm not going to lie.
"When they call him El Presidente, it's not for nothing. If he ran for president of Nicaragua, he'd probably win. He's an inspiration for our county."
Martinez, his elbow bothering him, had been released by the Seattle Mariners in May 1997 after going 1-5, and it looked like he wouldn't have a chance to pass Marichal. But Martinez changed his mind about retiring and got one final chance with the Braves.
Marichal, from the Dominican Republic, was critical of Martinez hanging on just to pursue the record. In the end, though, he sent a two-line congratulatory fax to Martinez. "It wasn't his voice, but it was nice," Martinez said at the time.
Chicago White Sox manager Ozzie Guillen was a player with the Braves in 1998.
"I know how tough it's been for Dennis," Guillen, from Venezuela, said at the time. "A lot of people didn't believe in him the last two years. I'm really happy. I know what this all means to him. I also know what this win means to Latin America and to baseball."
Martinez, who battled alcholism early in his career, got one more win that 4-6 season with the Braves and finished with a 245-193 career record. He never came close to a 20-win season, but won at least 14 games nine times.
Martinez led the National League with a 2.39 ERA in 1991 -- the year he pitched his perfect game for the Montreal Expos against the Dodgers in Los Angeles. The Expos scored in the seventh inning to beat Tom Morgan, 2-0.
It was the 13th perfect game in the Major Leagues, but the first by a pitcher from Latin America.
The perfecto set off celebrations in Nicaragua, especially in the capital of Managua and Martinez's hometown of Granada. Matching and then breaking Marichal's record also touched off unscheduled holidays.
Martinez tried to put the emotions of his countrymen into perspective for The Sporting News:
"They told me they were all screaming and jumping around and celebrating in whatever way they could. They forgot about how poor we are. They forgot about the need they have to eat. You know, you can fill up your stomach and not be hungry anymore just by being happy. That's the only way I can describe it."
Martinez was the pitching coach for the St. Louis Cardinals' team in the rookie Gulf Coast League this summer after serving as a special adviser for the Baltimore Orioles -- his original team -- the previous two years.
Braves bullpen coach Eddie Perez remembers Martinez fondly and appreciates having had the opportunity to be a part of the record-breaking victory as a teammate.
"We were all waiting for a long time," Perez, from Venezuela, recalled. "I remember the president of Nicaragua was with us for a while. It was a big thing."
Perez remembers Martinez most for his fearlessness on the mound.
"He wasn't that big and he wasn't that strong," Perez said. "But there were hitters that were definitely afraid of him."
Guy Curtright is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.