Two answers to this question.

The first game that my parents bought for me was Wing Commander from a garage sale when I was like six.

The first game I bought on my own was Freelancer when I was around fifteen via eBay.

Both were totally worth it.

That I personally bought?

Pretty sure it was King's Quest VIII: Mask of Eternity.

I think either gobliiins or starush for the Amiga

X-wing.

Majora's Mask. I preordered it and saved up allowance for months. It came to like $100 CAD with tax. Played the shit out of it and finished it in 2 weeks. The game was good, but I was quite disappointed because LttP and Ocarina both took me at least a month each. MM only has like 4 dungeons. Ended up trading it to a friend for Smash Bros.

Well, bought FOR me... Atari 2600 Combat (came with the system). I think I was 8 or 9? Totally worth it!

World Grand Prix for the Sega Master System 2.

Technically the second ever game I owned, as the system came bundled with Alex the Kidd in Miracle World.

Was maybe 6? at the time.

I remember my mom bringing me to Best Buy in spring 2004 right after I had gotten my Gamecube the previous Christmas. I bought Smash Melee and Mario Sunshine. I was 7 years old.

I had gotten games before then but those were the first two I was taken to the store to buy myself.

I still remember holding them as I walked down the aisle toward the registers. Aaaand that was the cheapest those two games ever got lol

Couldn't tell you the very first game I bought, but I definitely remember one of the oldest being either Ed Edd n Eddy: The Mis-Ed-Ventures for gamecube or Sonic Unleashed for PS2.

I could at least say with certainty my first Steam game purchase was most likely Portal 2 since I wanted the level creator super bad as an xbox port owner.

Had games before on the ZX Spectrum but probably Prince of Persia (original) on our first PC. But it was a pirated version as that was all you could get in the country I lived in. First boxed game I bought was Sim City.

I was about 8 or 9ish. And yes, to both.

This might not actually be the first one, but one of the earliest games I definitely remember actually buying with my own money was Geoff Crammond's Grand Prix 2. I would have been around 7 or so.

Definitely worth it, great game and the demos on the CD introduced me to Transport Tycoon, and the XCom and Worms franchises - and things kind of snowballed from there!

Xenon 2 Megablast for the Atari ST, with my saved-up pre-teen pocket money. Was it worth it? Fuck yes.

Stonekeep with my birthday money! It was fantastic.

Colecovision pong in the early 80s for console. Commander Keen would be my first for PC.

It probably would've been something on the Sega Genesis but hell if I know now

When I was ~7, I got a Super NES bundle that included both Super Mario World and Super Mario Kart, as well as a second controller. Absolutely worth it.

First game I specifically asked for from my parents: Stunt Driver. Must have been in the first half of 1990.

First game I saved up for and bought myself: Super Mario Bros 3. Much of the money I saved came in the summer of 1990, so that would have been in late summer of that year.

I don't remember, but it was one of those yellow cartridges the size of your palm. I think they were knockoffs. Can't say for sure.

It was a side-scrolling fighting game with tiny martial arts dudes. It could be played co-op. I think the bald character was overpowered, or I just felt like he was.
It was either a tournament style, attacking a rival dojo or both. Or something else.

I liked the cool art on the cartridge.

Sonic the Hedgehog for the Sega Genesis. Still one of my favorites so definitely worth it.

For my own allowance, it might have been a space shooter, Bosconian, on the C64. I must have been 12. The game was pretty bad unfortunately.

Croc

https://www.lemon64.com/game/skate-crazy

All was pirated, because nobody actually sold games. Some shops specialized in electronics slowly started having random C64 titles. This was one of the first ones I ever saw.

Never had actual original covers on any of my pirated casettes.

Game was shit.

First game I got or first one I bought for my own money? The first game I ever got and played was Super Mario Land for the GameBoy. I remember when the hype around Pokémon Red/Blue coming to Europe was building I was trying to calculate how many weeks of allowance I would need to save up to afford it, so that might have been the first one I actually purchased, I can't remember for sure if I bought it myself or got it as a gift. Diablo 2 launched a year later and I know I bought that one as I vividly remember the car ride back from the store, so otherwise that might be it.

All of these were of course incredibly worth it. I would never have gotten into video games without that GameBoy and Super Mario Land I think, and Pokémon was a formative experience for me as I got to participate in the whole Pokémania phenomenon. And Diablo 2 is one of the games I have the most hours in over my childhood, it kept resurfacing over my school years as me and the other gamers in my school would randomly get the urge to start playing Diablo 2 again randomly almost yearly over the course of like 8 years after its release.

Super Mario All Stars bundled with a SNES. I remember going to the supermarket with my grandmother to get it.

Jet Set Willy. It was on a cassette tape, for the spectrum computer. My brother's and I got probably hundreds of hours out of it.

I can't remember if I ever bought a NES game but I know I bought the SNES with turtles in time with my own allowance money when I was like 8 or 9. First PC games was Theme park and Transport tycoon deluxe bought at the same time.

Metroid Fusion. Such an awesomely replayable game.

Blackjack on the RCA Studio II.

A cassette tape for my MSX with 2 games by Konami: Hyper Rally and Antarctic Adventure. That was in 1988.

I've been gaming ever since.