Yea, and Twisted Metal! And Cool Borders, Crash Bandicoot, etc. PSX were good times, finally breaking into mature games. Well less mario, and fisher price. I remember having bad fighting games for PSX when I first got it, Battle Arena Toshinden, and Criticom. Fighting Force, Bloody Roar, etc came later.
Video of Criticom. I actually played this game a lot. I got it when I got the psx. It didn't floor me but I beat it with all of the characters I think. I played 2 players mostly. Good old PSX days.
http://www.youtube.com/watch?v=iXNo5ZwSYyo (Must be the Sega Saturn version, the PSX version looked better)
Edit: Ok, the dude that made the video above must have only played the game recently. This is a better vid. That intro brought back some good memories. This was an awesome game, I also had a game called Cyber Speed, a racer on rails. It had CG videos as well. Videos like that in games was new to me, and it was good stuff, no matter how cheesy it was. MGS1 just blew the roof off of videogame cutscenes. Man good times, and games have come a long way.
http://www.youtube.com/watch?v=9dNnKl5lm5Y
