GTA San Andreas: Before the series had no story, no dimensional character, no coherent missions, it had no brain but it just had sense of humor. GTA SA changed tons of shit about the series. It introduced a deep story, deep and tons of characters, missions with goal that makes sense for the story, tons of stuff to do and sandbox fun.
Red Dead Redemption: The previous game Red Dead Revolver was trivial linear arcade like shooting but this game made the Red Dead series have its current identity in a good way.
Need for Speed Underground 1: The previous games were just ordinary car racing, Underground changed the series into street racing and car customization series.
Far Cry 2: Previous game was more like pew pew action game but 2nd game established the core of the series' current identity but IMO after that it lost its "simulation" in favor of being a mix of also being a pew pew action game series like the first game.
Colin McRae Rally - Dirt 2: Until then it was an ordinary rally game, Dirt 2 made the series turn into "more than rally" stylish racing game with cool cockpit customization with toys and stuff.
Witcher 3: First two games were rather linear games, 3rd game was massive improvement however CDPR didn't care about this style of improvement on why the game is liked therefore they made CyberJunk 2077 more like Witcher 2 with open world that has Witcher 1 side stuff taste lol.
The Sims Bustin' Out (However I mostly mean GBA version): Sims was a series of life simulator without any goal per se, Bustin' Out changed it to life simulator with a "story" that has missions to complete in its own context and the Urbz in the City's GBA version improved a lot on that. This is how I would want new Sims games to be, beyond just playing parent and fake virtual life shit lol.
Prince of Persia: The Sands of Time: The series was nonsense platformer game and Sands of Time made the series actually matter by giving it a soul. Too bad Ubishit shit into the series since 2nd game and so on lol and they didn't release the Prince of Persia Redemption that would be a legendary POP game so me sad lol.