Like many, I suppose, VII and X are my favorites. If I could be perfectly objective about it, X is probably the better overall game. However VII has a big nostalgia factor for me. But unlike most things from my teens, FF VII actually lives up to expectations when I revisit it today. The first time I played it, I logged 35 hours of play in three days. You weren't some nameless cookie-cutter person just killing monsters looking for loot and power-ups. It had distinct characters that you identified with and cared about, an interesting world and setting, and a meaningful story. It was like the original Dark Forces that way. But Dark Forces was only able to deliver the cool story between long levels whereas FF VII had it suffused throughout ( though yes, there could be long sections of random monster encounters at times ). Those were some of the first games I remember that tried to be something more than just another video game. They brought a flair of the cinematic, but being longer than a movie were able to get a deeper, thicker story usually only in books. It was interactive cinematic literature. I'm not saying others didn't do it before, just that I didn't have them in my collection.
FF X was kind of like the perfect storm FF VII was. You had a new generation of console to power better graphics, awesome FMV sequences, cool characters, an exotic locale, a story you cared about, and all new voice acting. I think the battle system hit perfection here with the time-sensitive turn-based approach, hot swapping characters, and different tactics for different monsters ( just add the materia system ). Yeah, you still had some cheesy moments ( like that weird forced laugh sequence ), but you had some awesome heartfelt stuff too, like Tidus not being able to actually hug Yuna at the end, Tidus and Jecht's final high-five, and Yuna whistling on the dock at the epilogue.
Of course, if we're talking about the Final Fantasy universe, and not just FF games, then Kingdom Hearts wins ( KH II and BBS are my current favorites there ).