Yuffie and Vincent.

[Skyblade]

I managed to get Yuffie without having any prior knowledge as to how to recruit her, on my first playthrough (though I had to look up how to get Vincent).

I was making my way towards either Junon or Cosmo Canyon, and I got into a battle with her. I remember thinking "She looks a little too... human, for a random encounter enemy."

And you didn't wind up getting your money stolen on your first run in with her? That's rare...