I think it was the first Crash Bandicoot game.

Ridge Racer, Riiiiiiiiiiiidge Racer!

Resident evil 2.

I wanted a PS1 for Gran Turismo, Metal Gear Solid and Tekken 3, but only had enough money to buy a discounted bundle with Pro Pinball: Timeshock and Porsche Challenge.

I bought those 3 games at some point in 1999.

And because the PS1 got analog sticks in 1998 (Europe)

I never had the console, piracy run rampant in my country so there was no reason, most of my friends had it and bought a lot of games which were ultra cheap (around 1 U$), I bought a few fighters and a memory card and took them to my friends house when we scheduled a meeting.

Ridge Racer and Tekken, which I played only in amusement arcade, before it was released for the PlayStation. That was my reason to get the PS.

This game

Don't think anyone has heard of it, but it was the first ps1 game I played and couldn't have enough. I bought it solely based on the cover and because the rest of the games didn't look all that great to me. It was one of the best moments of my childhood, though now thinking about it, the game wasn't all that great. But it will always have a special place in my heart.

Spyro!

Ridge Racer and Battle Arena Toshinden. Both games were mindblowing at the time.

Also it was the first system I ever bought at launch.

This one game doesn't exist.
The complete PS1 line-up was much better than N64 and Sega Saturn line-up. This made me buy a PS1.