Crisis Core, just the Prequel we all needed!
Even if you've never touched a Final Fantasy game, you won't be lost in a series of cliches, in-jokes and references to past plots and characters.
People will rightly point out that the game does make some references to past games; FFVII cameos and events occur occasionally. Nonetheless, these moments rarely are integral to either the story or the gameplay. On the contrary, the game's plot is new, and as a prequel, the game's timeline fortunately precludes most of the drama and plot-twists of it's chronological predecessor.
This means anyone can pick up this game and be able to appreciate and understand the vast majority of the story. In short, the game is a stand alone novel, and while some background knowledge can add further depth to a few dialogues and events, even a novice will be able to follow the rather straight-forward story.
The gameplay is much the same vein. Many things--such as materia--will seem strange to newcomers, but the helpful tutorials (and instruction booklet) should help you overcome any confusiing parts of the game.
On the other hand, if you've played Final Fantasy games before--especially the seventh in the series--then you need no introduction to the game: it plays very similarly to FFVII (with a few minor tweaks for the PSP.)
Plot battles and CG movies are usually short, and perfect for a bus ride, waiting room, or any other brief moment during which you decide to use your portable gaming system. The main story itself is fairly robust for a portable RPG. I clocked in at around 20 hours, but I had neglected almost all of the side-quests, extra dialogues and the dozens and dozens of optional "Missions." Add those in and one can quickly burn 60 or more hours in a playthrough. As if that's not enough for a bargain game, you can even play a "Game+" mode which carries over some items from your previous save.
In conclusion, FFVII:Crisis Core is very accessible to new players, yet it offers enough fan candy that "veterans" to the series won't be disappointed. In addition,it's a great game, as most of the reviewers here have already said. It is fun to play, lengthy for a PSP game, and has lots of extras to keep its replay value above average. I highly recommend this game to any with a PSP; it's truly a must have game.
SPECIAL NOTE: There are some things to this game that you might want to take into consideration. I started playing this game on my old PSP then early into it bought the new model. The difference is HUGE. The load times on the new PSP are cut not only in half, but takes the load time from up to 18 seconds at some points to maybe 3-4 tops. There is also a very low amount of blur when Zack is running around on the screen on the new one compared to the old one. The new screen is brighter, higher refresh rate and the load time on the new one is way shorter. The new PSP is almost a must for this game otherwise load times will destroy the experience.