Two reasons: First, that $10 price point. You've likely got that kind of scratch between the cushions of your couch (and if you don't, you should probably look for a better couch).
Second, and more importantly, Persona 3: FES is arguably the best roleplaying game of the last two console generations. I'm willing to admit that its sequel (the aptly titled Persona 4) might improve on it in some ways, but this Wired review makes a solid argument as to why everyone with even the faintest interest in the genre should own the game.
Fair warning though, the game is long and incredibly deep. Expect to drop a minimum of 100 hours into it before you reach the end. And don't be surprised if, after playing, you immediately seek out the other half-dozen games and off-shoots in the series.
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