I've mentioned Persona 3 multiple times, and that is because I am in love with it. I'm late to the party, as I have just recently picked up the game. Persona 3 is ridiculously innovative; I can't say I've ever played a game like it. As such, I wanted to outline some of the highlights of the game (and copy Allistair, sorry about the shameless copy, it's retitled now :P), and why I like it so much.
1. Dating Sim Elements
I've played JPRGs, and I've played dating sims. I've never played a mixture of the two. Persona 3 has a day-to-day system where time passes and you have to choose how to spend your day. You can increase stats of academics, charm, or courage to open up different opportunities in the game. You can also choose to increase your "social links" which give power to the personas you create. This system immerses you in the game and makes you feel as if you are really living your character's life. To me, it feels like playing a manga as a video game, so if you're into manga, I'm sure you'd enjoy it.
2. Personas
I am an avid Pokemon fan. Personas share similarities to Pokemon. According to the game, personas are facets of your personality. You use them to fight in battle. Your personas can level up and learn new skills. However, leveling personas is a chore, and you are encouraged to fuse personas as opposed to leveling them up. Fusing personas yields different and stronger personas. The persona system keeps the JRPG battle system fresh and adds a lot of fun factor to the game. I could sit and try fusing different combinations of personas for a great length of time.
3. The Art Style
Despite being a Playstation 2 game, Persona 3 looks great. The cell-shaded-esque graphics fit the world well and still look great today. Some of the graphics of games from the last generation did not age well and can affect the enjoyment of a game, yet this is not the case with Persona 3. Its graphics have aged quite well.
4. A Compelling Storyline.
The storyline of Persona sucked me in early and I'm still engrossed in it. I find the story very interesting and I'm always excited to progress it further. While it may contain cliche anime tropes, it is by no means an overly trite story. I feel like this is a game that would not have worked without its plot. It is definitely an integral part of the experience.
I'm not quite sure how to state this last bit, but it's something that stood out in the game for me. At one point, one of the characters calls out the main character for being perfect, and how he does everything right. I've never seen a game acknowledge the invulnerability of a protagonist before, yet it's a trope that's seen in almost every game or series. This moment stuck out in my eyes as one of the most memorable situations in the game.
I do recognize that Persona 3 has flaws. If you are opposed to grinding, then you probably would not like the game. The battle portions of the game are pretty much one large grinding section. This is not enough to dampen the experience for myself, but I'm sure others may see it differently.
I may be rather late to the party with this post as well as playing the game, but I want to express what I like about the game. My hope is that someone will read this and give Persona 3 a shot. It's a game that has stuck out among many others in a very good way for myself, and I would like for someone else to be able to experience it as I did. If you haven't picked up the game and it sounds good, I strongly suggest playing it. You can buy it on PSN for $10 or hunt down the PS2 version, if that suits you better. Alternatively, you can buy Persona 3 Portable on PSN for the PSP.
Edit: The music. How on Earth did I forget the music? The soundtrack to Persona 3 is easily one of my favorite parts of the game, and one of the most remarkable parts as well. Its soundtrack is highly diverse and unique. I can't remember a game I've played with music anything like it.