Metal Gear Solid and Crash Team Racing come to mind. :)
I wasn't a huge PlayStation fan because of the ugly graphics, I still preferred the SNES style, but MGS, and to some extent Mortal Kombat 3 were games that made me want to own a PlayStation.
Tekken 3 and Driver I also remember playing.
And of course the Tony Hawk games.
I totally forgot about driver... what a game. Shame driver 2 didn't quite live up to the expectations though... although it was good
Driver was one of the best driving games on playstation. Somehow I never got to play Metal Gear games, I've heard nothing but the praises on that series.
Playstation graphics were also sometimes off-putting to me, they kinda look like blocky metal sheets melted together.
Well, there are definitely reasons to be critical of the Metal Gear series, trust me. :p
I was into them for the story, for the most part. As games, they fall short on some aspects. The controls and camera can be very clunky.
Metal Gear Solid 3 is probably my favourite in the series, it was slightly remade for an HD collection that they released, and includes improvements on playability, you should check that out if you're ever interested.