Any of the Final Fantasy games.
(And now, please excuse me as I give a reason for this to hopefully avoid being flamed down for not being in the majority.)
The fan base is huge and I can see why some people would be interested in it but I'm more of a fan of substance over style, and substance is probably the main thing any of the FF games are lacking in. Overall nothing has really drastically changed in the way any of the games played and because of how all the main characters were Mary/Gary Sues/Stus I couldn't really hold any sympathy for them or give a crap about their quest. The basic elements of gameplay don't feel visceral or involving enough for me to fully (sorry for using a Yahtzee term, people) immersed in the gameplay because I have to select everything from text boxes and all that does is remind me that all I'm doing is selecting a bit of code to start an animation and calculate some statistics.
On the flip-side, take a look at games like "Space Quest" or any of the other text-based adventure games. I found these a hell of a lot more immersive (there's that word again) and they're pretty similar (okay not that similar, but bare with me); they're story driven and they're mostly animations, coding and statistics selected by basic text boxes. The only difference is that you don't need to worry about the stats since they're not RPGs. I loved these games because the stories were compelling, the characters were likeable and interesting and what little combat they had (giant robot fight at the end of Space Quest 6, anyone?) had some contribution to the plot and had a reason as to why it happened which lead to giving the characters more depth instead of random encounters that served no real purpose.
Now flame me for that flawed comparison, I know it sucks but it's the best I could do since I've not really tried any other JRPG. I could've compared it to Oblivion or Fallout but that's still flawed as a comparison and someone will point it out, so it's kind of Catch 22 either way. I'll do my best to answer any objections you may have with my comments here but please keep it civil. Thanks.
EDIT I just remembered something to compare it to that I actually enjoyed and was very similar to Final Fantasy. I loved the Ultima series and they were basically random encounters, text boxes and story-driven gameplay, but the main difference was that I felt like I was actually playing a role since a lot of effort was made to make the world I was exploring as believable as possible and the entire game was nothing more than 8-Bits of fantasy pixels. Also, I now realized that I need to dig out my old Master System.
INB4:
"You're just a biased Xbox fanboy!"
Your point being? When someone asks you a question that asks your personal opinion then obviously you're going to be biased. I tried to get into FFVII, FFIX and FFX but they just aren't what I'm looking for.
Even though I own an Xbox, I'm no fanboy, I just prefer some games over others and Microsoft has what I like. I own (and still play) a SEGA Mega Drive 2 if you'd like to have a go at me about that, or how about my love of Tetris, Bejewled and Bust A Move 2?