I got 4 when I got my PSone:
Croc
Bugs Life
Steam Boat Mickey (I think that was the name anyway)
And Crash Bandicoot (I was bloody amazing at that for a 5 year old)
But, I can't remember which came first for me, the PSone or the GameBoy (you know, the old 4 AA battery ones), in which case, it was a broken Pokemon Yellow, shortly followed my a Mario game, can't remember which one, I was gutted when I lost that (The second level had a Sphinx (I think) at the end, which shot fireballs at you. And I severely regret throwing all of the aforementioned items away. The sentimentality of it all is killing me.