If you played Persona 3, enjoyed it, and haven't played Persona 4 yet; stop reading and get this game now. Persona 4 mostly keeps the same level of quality as the previous game and sometimes even surpasses it in some aspects. With that said, onto my review.
Persona 4 is at its core is a JRPG that consists of mainly two parts. These two parts are the dungeon crawling portion, and the social interaction part. The dungeon crawling part involves your party going through various dungeons basically beating the crap out of shadows, the main enemies of this game. The battles are typical Shin Megami Tensei fanfare, turn based combat that rewards exploiting enemies' weaknesses with extra turns and attacks. The combat is pretty much as streamlined as turn based combat can be. One improvement that Persona 4 made over Persona 3 is the ability to directly control everybody aside from the main character. While this does make the battles longer than they were in Persona 3; it beats HOPING the character AI will do what you want them to do.
Keeping true with the series, personas make triumphant return here. Personas are the avatars that the playable characters use to cast magic and personas also dictate their strengths and weaknesses. The main character also has the ability to switch between multiple personas that you can catch and fuse. The fusion system can be used to essentially make custom personas and a player that really invests themselves to this system will be rewarded with Personas that are built for their play style.
The big thing that separates the recent Persona entries from every other JRPG out there is the social interactions in game. While there are NPCs in every RPG that you play that you can talk to, in the recent Persona games they actually affect how powerful the personas you create are. These social interactions with these characters also help deepen the story by providing subplots outside the main plot. One neat thing that occurs with these interactions is the manner in which they intertwine with the story. This has a very immersive quality as everything connects to another within the story. The story plays out like a murder mystery within the confines of a small Japanese town with some dangerous TV dimension thrown in for good measure. The story also does not require the player to have any knowledge of what happened in Persona 3, though there are nice cameos and easter eggs for those that have played Persona 3.
Personally, I preferred the Persona 3 story. While Persona 4 is certainly more palatable with its story, it just didn't have the trademark Shin Megami Tensei atmosphere of being constantly messed up. That was what really drew me to Persona 3 and the Shin Megami Tensei series in general, and was a little bit disappointed with the mostly light-hearted atmosphere. This is a fairly minor gripe though and really didn't take away from the great story in the grand scheme of things. That and Persona 4 is quite simply mechanically better than Persona 3 was
All of these make Persona 4 an excellent place to start for people new to the Persona series. Persona 4 is more than likely the best JRPG of 2008 and should be an instant buy for fans of the genre, and a game to check out for those people that haven't played many JRPGs to sample the best the genre can offer.