I bought Xbox day 1 because I was convinced by magazines. Halo definitely sealed the deal though. 

Same.

Even tough there was the prospect of a Kingdom Hearts 3 on PS3 as well. But FF versus 13 at least had a trailer to go off of.

Picked up a PS4 for Final Fantasy XV
Picked up a PS1 for Digimon World
Picked up a Gamecube for a couple of Pokemon and Sonic games iirc

N64 - Mario 64. The N64 was my first console. I had played a lot of NES games at my neighbors house before and Super Mario Bros. was the coolest game they had. When I saw the commercials for Mario 64 and later played it at a friend's house, I absolutely had to get that console. I remember Mario looked so huge on the screen and when I played the game with a bunch of other kids at that friend's house we kept dying over and over again on the first bridge in Bob-Omb Battlefield lol.

Nintendo DS - Super Mario 64 DS. Well, I loved the N64 version and back in 2004/05 it was just mind blowing that such a game could run on a portable console. I also bought the console for Mario Kart DS.

Wii - Wii Sports and Twilight Princess. Zelda as a launch title was amazing, but it was the motion controls of the Wii that really made me want to own one. I remember I had a huge smile on my face the first time I played Wii Sports, thanks to the combo of the motion controls and the built-in speaker. The Wii years were my favorite years in gaming because for five years or so we played every multiplayer game on that console to death with a large group of gamer friends. So amazing.

Xbox360 - The Elder Scrolls IV: Oblivion. Oblivion looked so amazing, it made me buy a 360. I didn't like the game as much as I later liked Skyrim, but it was still an amazing experience. I would also sell the 360 and buy a PS3 instead, but I didn't buy that one for a particular game.

PSP Go - Sony's PSN deal. Back in the day when the PSP Go bombed hard, Sony gave away ten (!) full priced games with the purchase of every PSP Go for a time. I got Jak and Daxter, Ratchet & Clank, Motorstorm, Gran Turismo and even God of War (I think) and I only had to pay 99 Euro for the console in a clearance sale. Best gaming deal ever, I loved the PSP to death. So sad Sony left the handheld business. I always preferred their handheld games to their home console games.

Switch - Breath of the Wild. I plan to finish my second play through of the game later this month. One of the best launch titles ever and one of the best games of all time. The experience was magical. Still remember chilling on our couch on the balcony, playing the game. Jeez, can't believe that was already 5 years ago.

Pokémon. Except for the Switch, I never bought a Nintendo handheld until it got a new Pokémon game.

Also, Twilight Princess for the Wii. So hyped for that one I asked my parents for a Wii like a million times. And let me tell you: the game survived the hype. Still my favourite Zelda ever.

Rogue Squadron - N64
Rogue Leader - GameCube
BotW - Wii U (yes! :D )

I didn't buy many consoles in the earlier gens (most were given or gifted) so that counts me out on several generations and the more current ones (say 6th/7th and 8th) I didn't buy for singular games..

However I did base my decision to buy PS5 early in the generation for God of War Ragnarok. Also anticipating Naughty Dogs next title - and new IP.

I was so upset with Nintendo durimg the Wii u era that I said i would never buy another nintendo console. But then came breath of the wild.

Bought a PS3 Ultra slim to play GTA V
Bought a Wii Mini to play Super Mario Galaxy 2
Bought a PS4 to play God Of War
Bought a Switch Lite Palkia/Dalgia to play Pokémon Diamond remake

Final Fantasy VII made me buy the PS1.
Metroid Prime made me buy a GameCube