This is a good topic I don’t think I’ve seen before. Well done, OP!
I’ve done my best to take this question as literally as possible, and list what I consider to be defining games, not necessarily my favourites or what I consider the “best” games.
2nd gen
- E.T.
Yes, it sucked horribly, but it also summed what I think of this gen as a whole. I know there were plenty of good games, but I also remember none of them ever interesting me for more than a few minutes, and as a young child I had no interest of asking my parents to purchase one of these systems for me. ET was, and is, emblematic of a gaming generation that I couldn’t take seriously, then or now.
3rd gen
- Super Mario Bros.
This is the defining game of the entire hobby for me. It brought me back, it made me realize gaming was fun and not a novelty. For the first time, I had to have one. I played this game over and over at our local K-Mart while my mother would be shopping.
4th gen
- Chrono Trigger
This one is also my favourite game from my favourite generation. So many great games for SNES and Genesis (and to a lesser extent, TG-16), but this one solidified everything that made this gen great. Bright, beautiful sprites, gorgeous music, and a console RPG with (then) many unique features, including multiple endings meant to be seen via the “New Game +” mode.
5th gen
- Metal Gear Solid
Suck it, Ocarina of Time. MGS was, and still is, a master class in fun gameplay, novel mechanics (the massage via the rumble feature, Mantis reading the memory card, etc) and of course, probably one of the best, mature attempts at real storytelling. It’s quite actually the game that got me into this generation, as not even the mighty (and overrated) FF7 could get me to buy in.
6th gen
- Grand Theft Auto III
San Andreas is the better game, but we wouldn’t have open world, sandbox gaming at all without this groundbreaking title. I played the original GTAs on PC, and yes, though fun, they were also tedious. Bringing those games into the third dimension, providing countless, enjoyable side distractions such as optional missions and collectibles, and pulling zero punches with respect to its subject matter, while also retaining a great sense of humour (something most “grim n gritty” titles seem to forget) make this one I can go back to even today, blocky graphics and all.
7th gen
- Grand Theft Auto IV
I. HATE. THIS. GAME. It’s awful. The driving mechanics are impossibly floaty, the palette is far too brown, the story is just boring, and the silent protagonist in III has more personality than this jerk. It also ranks among the highest scored games ever on Metacritic (R.I.P. gamerankings.com). Why am I listing it as the “defining” game of the genre? Because while I was growing up, the gaming press was not, and what’s worse, they all appeared to be in cahoots with each other just to rank this one highly “because it’s GTA and it’s so realistic, it MUST be better than the games that preceded it, which we also gave high scores too.” More is not always better. Everything they did to make this “better” to take advantage of the new hardware made it worse, and then they forgot to even make the core game any fun. As far as I’m concerned, this game should be buried next to ET in the desert. Burn it.
As an aside, in the same generation that Rockstar released this turd, they also made their best game ever, Red Dead Redemption. However, even this great game can not overcome what to me was the defining badness of GTA IV, and the clear exposure of an ever present, flawed gaming journalism.
8th gen
- Star Wars Battlefront II
Look, this was one of the best generations of all time, as far as games go. I’m very, very happy with all the great titles that have been made..... but nothing, nothing can define this genre more, to me, than the sea change towards selling incomplete titles at launch (even going so far as to strip content) and sell it back to the customer for more money, the cynical approach to DLC, and of course, the god awful rise of microtransactions, even to the point of literal gambling.
To be fair, A LOT of titles this gen suffered from at least one, if not all, of the above boners. And while Star Wars Battlefront II may not be the most egregious example, AFAIK, it was the most visible (especially regarding micro transactions and gambling).
And we only have ourselves to blame for this mess. Way to go.
9th gen
- Legend of Zelda: Breath of the Wild
I’m currently playing it, and 40 hrs in I’m not only barely scratching the surface, I’m not even remotely tired of it. I want to keep going. As young gamers in the late 80s, my friends and I would always ask the “wouldn’t it be cool if....?” questions about our favourite games, like what if you could do THIS, or if you could do THAT, especially in RPGs, especially in Zelda titles. Link to the Past is the ultimate 2D Zelda title. As a father and husband who enjoys games, Nintendo has made manifest in BOTW what my imagination always hoped LttP could be if the technology were ever there. It was impossible then, and it even still seems improbable now. Not the open world (that’s been done ad nauseum), but an open world rich with all the details, lore, and questing that made the Zelda franchise so beloved in the first place.
BOTW isn’t genre defining to me because I love it (which I do), but because it also served to put every other game developer and publisher on planet Earth on notice: Nintendo can do “your” genre, and it can do it better than you. I see your western open world game and raise you with THIS.
ADDENDUM: yes, I know BOTW was also released on Wii U, and for the ten people who bought that system, congratulations. For the rest of us, this is a Switch title, and the ability to just pull the Switch out of the dock and continue playing the game in handheld mode without waiting, really helped highlight the brilliance of this hybrid platform.