I absolutely love the Persona series, though I've only ever finished Persona 4 and Golden. I'm currently crawling my way through FES (though I just got the undub so my progress might speed up), and I'm somewhere at the beginning of 2 (Part 1) and 1, but I'm hoping to finish 'em one day.
My favorite (and first) Persona game was Persona 4 (and later, Persona 4 Golden). I just absolutely loved the characters in this game. The game went out of the way to create these characters whose problem's were very real, as were their personalities, and because you spent so much time with them, they connected with both the player and the MC on a personal level. The story was great as well, and I especially loved the twists and turns it often took, without ever trying too hard to be incredibly shocking.
My favorite character? Well, Marie's up there, since she was such an enjoyable addition to the series (and she was cute as well, especially in terms of personality). I also really liked Kanji, largely because of his character but also because of his voice actor's performance, they just blended together so well to make a believable character.
Persona 4 was my entry into the Shin Megami Tensei series, and I bought it back in 2008 because my friend wouldn't stop telling me how good it was. So I bought it, got stuck, and sold it. I wasn't used to a Turn-Based RPG that was so difficult...that's what I thought at the time, at least. I really enjoyed the outside-of-battle portions, but the dungeons just crushed me again and again. About a year or two later I picked it up again and started from the beginning, this time using the fusion mechanics and what not, often trying to finish the dungeons in one day or two days rather than spreading it out over a few days or waiting until the last day. Just taking advantage of the fusion mechanic made and not skipping entire floors made it all so much easier, and the game became...not a cakewalk, but not difficult, either. I don't really know what changed in me to make me do that, probably just started thinking more logically. But the best part was that I was having fun in the dungeons now, and I was having fun in general.
Interestingly enough, SMT:Persona 4 wasn't my first SMT game, that title belonged to Demikids which, for the longest time I didn't even know was a Shin Megami Tensei. Regardless, since Persona 4, I've had an avid interest in the SMT games, and I've played quite a few of them since. It's a great series, and it's introduced me to different religions and folklore, and just has great gameplay in general, so I guess that'd be the reason I play.