Not in any particular order:
Street Fighter EX2 Plus: The game that made take fighting games a step further. Command lists were such a rarity in the PS1 days, so this game having one helped me tons in my early years. Plus the game is super fun and the combos feel really satisfying to pull off. I still love this game to this day.
Dino Crisis 1: Could have been any PS1 Resident Evil, but DC1 takes the cake in this one. I have tons of fond memories of it. I like how the game uses 3d backgrounds and environments in a better way than Code Veronica would a year later (the backtracking is also SOOOOO much better). The puzzles, despite having a lot of them, they make sense, and the different paths add to the replay value. DC2 is alright, but I like the more grounded approach DC1 has. Plus Regina is hilarious. xD
Tekken Tag Tournament: As much as I detest Tekken nowadays, I gotta admit this is one of the best fighting games I ever played (still doesn't beat EX2 though). It's Tekken 3 in its final form, polishing what's already there, while giving the Tekken 2 characters a nice update. It's all downhill from here IMO.
The King of Fighters XI: Could have been 98UM, 2002UM, even SVC Chaos. But I picked XI because this is where I felt the series take a risk. 2003 tried, but a ton of things were missing. XI is where they polished a ton of things 2003 brought to the table. The active switching system, while it looks very similar to MVC at face value, works somewhat different and doing combos while switching characters looks incredible. Plus it has my favorite set of midbosses in the entire series. Magaki is mad cheap, but beating him is really satisfying.
Test Drive 6: Something that's not a FG for a change. Is this game good? No. Is it polished? Also no. Is it funny? YES. This might be the funniest racing game I ever played. The physics make the cars look like they're filled with helium, and the crashes are absolutely hilarious. And the AI is just as much of a madman as the players, whether it's crashing onto traffic, or themselves. This game has nothing on a Gran Turismo 2 or Crash Team Racing (an honorable mention, love that game), this game gives me very fond memories and gave me many laughs.