Hmmm... Old memories...
The first one I played was Pro Evolution Soccer 2 in a friends' tourney. Making PES tourneys became a weekend role for years among all us (friends, classmates and neighbors), but I still didn't had my own PS2 console with any games (stuck with my old PS1, my first PC, the studies and some temporary jobs).
Finally, some years later, my bro and I decided to get our own PS2 with some uptodate games. It was the new slim silver model bundled with Moto GP4, and we also bought Tekken 5 and Resident Evil 4 at once.
Tekken 5 quickly became the favourite videogame at home, only later matched by PES 6....
By reminding myself of all this, I personally think that multiplayer videogames will always be the very best way of videogaming...