It's pretty safe to say that Persona 3 isn't for everyone, but fans of RPGs (either Japanese or Western) will likely get a kick out of its unique gameplay style and interesting, if somewhat emo, storyline.
The gameplay itself is a nice break from traditional exploring and questing, and is divided into two parts: dating sim social interraction, and turn-based dungeon crawling. The dating sim elements of the game, while allowing you to create more powerful personas that the protagonist can use in battle, really serves as a great break from the somewhat repetitive dungeon crawling and exploring in Tartarus, a modified version of the protagonist's high school that only appears at night. While the fighting can become a bit repetitive at times, especially toward the end of the game, battles are almost always, thankfully, quite short.
The AI for your party members, who you don't have direct control over, is actually quite good. You can issue general commands to individual party members, such as "heal/support" or "knock down enemy," but in general, you won't need to do much of that early on at all -- they'll generally just use their best attacks, do as much damage to enemies as they can, and heal themselves or other party members if their HP gets too low. The AI isn't perfect, however, and I found that there were several annoying problems with it. First, the party members do not understand damage reflection at all. If an enemy has a spell that will allow them to reflect any damage done by you or your party members for a certain amount of turns, they will all continue to attack that enemy, regardless of the fact that they may be putting themselves at risk. The only way to get around this is to tell them to stand by or wait. Second, in general, especially toward the end of the game when they have gained many of their passive or support abilities, your party members will almost always be preparing for a long battle. Instead of attacking, they will often cast buffs, de-buffs, and attempt to inflict enemies with ailments that are really only useful in boss battles. While this isn't really a huge issue, it may force you to go back to the entrance of Tartarus more often to charge up their mana (items that restore mana are pretty rare in this game and shouldn't be wasted on regular grinding if you can avoid it) which, in turn, will lead to having to repeat floors when you either don't really need to or don't feel like doing it.
While this all makes the battle system seem pretty simple, it allows you to experiment a lot with different Personas, which is where the combat/ability depth really comes from in this game. It's fun to try to create a personal lineup that will suit all of your needs and provide the protagonist with access to all of the elemental attacks, which you will need if you want to knock down your enemies -- the best way to win battles in this game.
The story in this game is very interesting, although I'd say that the pacing is a bit off. For the first 50 or so hours, you are handed plot points at an almost agonizingly slow pace. In November and December, however, there is a major plot twist and nearly all the mysteries of the situation are explained. The last 30 or so hours of the game, then, are essentially about you and your team mates preparing for the final boss battle, rather than learning anything new about Tartarus, the Dark Hour, Apathy Syndrome, or any of the strange things that are occuring in the environment. This is a bit disappointing due to the fact that the story leaves a lot of issues, such as the Strega and why they were created (other than a rather brief bit of information that you get from one of their members toward the end of the game) unexplained.
This is not to say, however, that the story isn't good. While I wasn't wild about how the information was doled out, the plot twists and explanations in November/December had a great affect on me. In fact, I found myself wishing for simpler times when all I had to do was make friends at school and fight with my teammates at night. It probably sounds a bit silly, but if a plot can affect you that much, it's probably doing something right. I was also surprised at how strange it felt to engage in the dating sim elements, or social links, after the plot scenario was completely revealed to me. Here I am, a regular highschool student, who is attempting to help Keiuske decide whether he wants to be a doctor like his dad or go abroad to study music, and I'm essentially deciding whether or not I might want to try and stop the apocalypse.
Heavy stuff.
This is likely an unintended consequence of the linear nature of the Social links, but it totally worked for me, and really made the enormity of the decisions that the protagonist had to make, hit home.
So, all in all, if you've got a lot of free time (because this is a pretty long game -- I've seen reports of people putting in over 100 hours, though I finished in about 85), and like RPGs, this game is definitely for you. I've given it 5 stars, despite its problems, because it is definitely better than the sum of its parts. It's definitely worth a look, especially given the budget pricing and epilogue offered by FES.