I guess I'm odd, since I'm a Rapidash person. :)
I've never really had an affinity for either Ninetails or Arcanine, though don't get me wrong -- I like both. I just love Rapidash. It might be that I've always loved horses/unicorns/pegasus and that's just a girly side to me. XD I think if I had a choice to have one of the three, I could make the most out of Rapidash. I'd be riding it all day, everyday! :D
In Pokemon Platinum, I ended up catching a Ponyta, which later evolved into Rapidash, and used it throughout the game. It was a male though, and I named him Dash. I always pictured Ponyta and Rapidash as females though, so I made up this story in my head (because, heaven knows, I'm not dorky enough already lol) where my Ponyta was the dominant male of a herd, and my character was lucky enough to befriend him, so he passed on the leadership to a younger generation.