Sonic 3 & Knuckles -
I could follow the pattern of the latter portion of this list, since I still buy and love Sonic games, but 3 & Knuckles is where it all began. Growing up on the Genesis/Megadrive, I did play all three of the games (and Spinball and 3D Blast, as it happens), but this one was the game that really grabbed my attention. Multiple ways to play the game with character-specific paths, a co-op function with Sonic and Tails together that opens up paths not normally available in Sonic's route, and just fantastic aesthetic design and music. Any love I have for games like Banjo-Kazooie, Donkey Kong, Kirby, LittleBigPlanet, or any other platformer stems originally from this game.
Pokemon Red/Blue -
Again, I still mostly enjoy Pokemon, but Red/Blue were by far the most influential on me. It was my introduction not only to handheld gaming, but also to RPGs in general. I had played Betrayal at Krondor previously, but being as young as I was I never knew what to do. Pokemon allowed a simple enough system and world that I could lose hours upon hours in it. Other RPGs like Final Fantasy VII/IX or Star Wars: Knights of the Old Republic may have left more of an impact on me for their stories and graphics, but I don't know what they would have been to me without Pokemon first.
Mass Effect (Franchise) -
There are precious few modern games I've played through multiple times. The number of them over 15-20 hours in length drops even further. Reduce it even more when you add in an entire series of games instead of just a singular title, and Mass Effect is practically the only thing left, joined by the ranks of Batman: Arkham Asylum/City and the Bioshock franchise (which are shorter) and Kingdom Hearts. Each game has its problems, undoubtedly, but taken as a whole Mass Effect makes up something greater than I could've ever imagined before having played it.
Metal Gear Solid (Franchise) -
Quite simply, it's the reason I've gotten into stealth games. I've only gotten into it recently (2011) as with many other games I missed over the years, but aside from the crushing difficulty due to my ineptitude I'm not sure there's a single thing I don't like about Metal Gear Solid. Even the ridiculously long-winded and overblown exposition is charming. And since it led me to the likes of Deus Ex: Human Revolution, Dishonored, and Mark of the Ninja, I can't really hold anything against it.
Kingdom Hearts (Franchise) -
I've made console purchasing decisions based on this franchise. I'd be liable to buy a PS4 solely for Kingdom Hearts III. They are the only JRPGs I've ever come seriously close to 100%ing (though stopping short at ~97% each time because the last few things constantly and consistently wreck me). Tetsuya Nomura is the sole reason I have any hope for Final Fantasy XV. So yeah, while they may not be my favorite individual JRPGs or anything (beaten out by Final Fantasy IX and Persona 4 Golden), taken as a franchise Kingdom Hearts may well beat out Sonic the Hedgehog at this point.
Honorable mention to Steins;Gate -
While it hasn't been quite as influential on my gaming habits (mostly opening the way to things like BlazBlue and Zero Escape, which I may not have otherwise played), Steins;Gate stands out as the only game to have ever pulled me in to another realm of media and entertainment: It's the reason I began watching anime. Now, I don't know if I'll ever seriously follow any anime (I barely follow television anymore), but a year and a half ago the only ones I'd ever even seen were Pokemon, Digimon, Yu-Gi-Oh, and Dragonball Z. Now I've watched enough that I have a hard time recalling all of them on the few occasions I'm prompted to think up a list. So, yeah. Fantastic job, Steins;Gate.
I could follow the pattern of the latter portion of this list, since I still buy and love Sonic games, but 3 & Knuckles is where it all began. Growing up on the Genesis/Megadrive, I did play all three of the games (and Spinball and 3D Blast, as it happens), but this one was the game that really grabbed my attention. Multiple ways to play the game with character-specific paths, a co-op function with Sonic and Tails together that opens up paths not normally available in Sonic's route, and just fantastic aesthetic design and music. Any love I have for games like Banjo-Kazooie, Donkey Kong, Kirby, LittleBigPlanet, or any other platformer stems originally from this game.
Pokemon Red/Blue -
Again, I still mostly enjoy Pokemon, but Red/Blue were by far the most influential on me. It was my introduction not only to handheld gaming, but also to RPGs in general. I had played Betrayal at Krondor previously, but being as young as I was I never knew what to do. Pokemon allowed a simple enough system and world that I could lose hours upon hours in it. Other RPGs like Final Fantasy VII/IX or Star Wars: Knights of the Old Republic may have left more of an impact on me for their stories and graphics, but I don't know what they would have been to me without Pokemon first.
Mass Effect (Franchise) -
There are precious few modern games I've played through multiple times. The number of them over 15-20 hours in length drops even further. Reduce it even more when you add in an entire series of games instead of just a singular title, and Mass Effect is practically the only thing left, joined by the ranks of Batman: Arkham Asylum/City and the Bioshock franchise (which are shorter) and Kingdom Hearts. Each game has its problems, undoubtedly, but taken as a whole Mass Effect makes up something greater than I could've ever imagined before having played it.
Metal Gear Solid (Franchise) -
Quite simply, it's the reason I've gotten into stealth games. I've only gotten into it recently (2011) as with many other games I missed over the years, but aside from the crushing difficulty due to my ineptitude I'm not sure there's a single thing I don't like about Metal Gear Solid. Even the ridiculously long-winded and overblown exposition is charming. And since it led me to the likes of Deus Ex: Human Revolution, Dishonored, and Mark of the Ninja, I can't really hold anything against it.
Kingdom Hearts (Franchise) -
I've made console purchasing decisions based on this franchise. I'd be liable to buy a PS4 solely for Kingdom Hearts III. They are the only JRPGs I've ever come seriously close to 100%ing (though stopping short at ~97% each time because the last few things constantly and consistently wreck me). Tetsuya Nomura is the sole reason I have any hope for Final Fantasy XV. So yeah, while they may not be my favorite individual JRPGs or anything (beaten out by Final Fantasy IX and Persona 4 Golden), taken as a franchise Kingdom Hearts may well beat out Sonic the Hedgehog at this point.
Honorable mention to Steins;Gate -
While it hasn't been quite as influential on my gaming habits (mostly opening the way to things like BlazBlue and Zero Escape, which I may not have otherwise played), Steins;Gate stands out as the only game to have ever pulled me in to another realm of media and entertainment: It's the reason I began watching anime. Now, I don't know if I'll ever seriously follow any anime (I barely follow television anymore), but a year and a half ago the only ones I'd ever even seen were Pokemon, Digimon, Yu-Gi-Oh, and Dragonball Z. Now I've watched enough that I have a hard time recalling all of them on the few occasions I'm prompted to think up a list. So, yeah. Fantastic job, Steins;Gate.