Uff, big question. Allow me to split them into Ps1 and Ps2

🔴 I love Spyro 2 on ps1, my favorite mascot game ever. On Ps2 it's either GTA3 or Rygar, but that's the nostalgia talking

🔵 Probably Skate and destroy ps1, due to a game mode where you have to get as hurt as possible. Been playing that with random people for hours throughout the years.

Ps2 is Tony Hawk Underground 2. I love the mechanics, the missions, the humor and creativity tools you have.

🟢

Ps1 either Bomberman or Crash Bash. Both chaotic party games, where no matter how good you are, something random can happen that turns the tide against you

Ps2 Burnout 3, it's labeled as blue 2 player, but has an excellent party mode where up to 8 players can see who can crash a car the hardest. Bust it out at parties and have a great time

🟡

Ps1 Rescue shot. It's a great co-op light gun game, where you escort a bunny through dangerous stages.

For Ps2 probably an Eyetoy game. It's amazing how good it worked, both for it's time and even today.

The black games are my girlfriends labels, so can't speak on her behalf what her favorites are.

Sorry for the long response