Not a game, but the first console I bought day 1 was Switch 2. (And with Mario Kart World and Fast Fusion at launch I suppose)

My parents bought us out SNES/N64/OG Xbox when we were kids/teens, I picked up a Wii and 360 in 2009, then a Wii U in 2013 once Mario 3D World came out, as before that there was nothing that grabbed me. I felt burned my the Wii U, so I didn't buy a Switch 1 until October 2017, once it became clear it wasn't another dud.

Switch 2 however I had to have day 1, just cos the switch 1 generation lasted so long and I was chomping at the bit to jump into the next generation.

Purchased myself? Not sure, but it was likely a Genesis game. But the first game that I got at launch was definitely Super Mario Bros 2 on the NES.  It was the first game that I really anticipated and I ordered it from a catalogue before it released.  I actually received the game about a week before any of the stores in my town had it and was maybe the first kid in my school to own it. 

No clue. It was so long ago. Maybe SMario 64 or Star Fox 64? One of the earlier N64 games gotta be it.

I'm pretty sure it was God of War III back in 2010, I was in college and tried to buy it in Sainsbury's but they refused because I was under 18, so I went to a local game store and they had no issue selling it to me :D

I think it was Mortal Kombat 2. We were at a mall (it was 1994, and malls were still a thing), and there was this little kiosk game-store vender. I walked up to it with my parents, saw they were allowing people to reserve the game (pre-orders were a new concept to me at the time) and begged my mom to do so. She agreed. I can't remember how long the wait was until it launched but man... did it seem like forever. When it finally came out, it was nothing MK2 for a good long while.

Ocarina of Time.

Honestly I don't think I got any games exactly on release as a kid. Smash Bros Brawl is the first game I remember feeling hyped for before it released but I'm not sure we got it exactly at release. Same story for some of the early WoW expansions. The first ones I'm pretty sure of are CoD Modern Warfare 3 and Diablo III. Even today the number of games I've gotten at launch is probably not that high, closer to ten than twenty.

Probably Harvest Moon on SNES. I was really hyped for that game, saved up for it and everything.

Likely Pokemon Gold or Silver.

Might've been Resident Evil 3. I actually got it a day or two before release from an independent seller in a little market stall.