I first played FF7 at a friend's house; his mother had bought it for him as a present and he hated it. He was unable to understand it or really play it, so he offered it to me. After five minutes of not knowing what I was doing I turned down the offer.
FF8 came out to reasonably rave reviews (granted less so than those of FF7), so I decided I had to give it a go. I rented it, played for a few hours, made absolutely no progress whatsoever and promptly bought it. I utterly adored it, it was probably the single most defining gaming experience ever for me. The characters, the story, the effects, the side quests, this game had it all to me.
FF9 emerged and was a return to what people seem to consider the 'true' FF genre, with castles and damsels in distress, but it was the technology of FF8 that had appealed to me greatly, so I skipped on 9.
FFX was the first foray into the world of 128 bit and my god, was I staggered. My friend had warned me that Tidus' voice was nasally American, but from the moment I heard the characters start speaking, played through the opening section, I knew this was something special. Everyone complains about the girlyness of FFX-2, and it's indeed a large departure from the FF formula, but I need closure after crying my way through the ending to X, so I'll buy it sometime soon.
In response to an earlier question, I've beaten all of the dark aeons and defeated Penance, but I don't think I've actually gotten around to trying Omega Gold yet, I should do that this evening.