What a nice trip down gaming memory lane. I was in about the exact same situation as you, owning ps1, ps2 playing mostly single-player games. But all my friends(and my cousins, lol) also had it, just as for you, and those memories playing nintendo 64 with smash brothers, kirby and pokemon arena was awesome!
Can't even compare online gaming to that feeling, that was what really caught me at a young age. It was so social and "alive" back then, i hope more games start to focus on nice co-op experiences.
The last one i had was the GoW series (awesome co-op gameplay) which i played with a friend at a bit later age, smoking weed and cutting locucst in half with a chainsaw...
God damn it i need a time machine right god damn now....
Good times for sure. I'm hoping the switch is going to make co-op gaming awesome again! If you want a great co-op game for PlayStation though Little Big Plant is amazing, and it's super fun with friends to play survival mode levels on the "user created" levels area.