The stories give more meaning to everything and make you grow more attached to the characters and consequently the game itself. A lot of other genres skip out on the story or minimize it and instead focus on gameplay or multiplayer or other stuff, whereas SOME JRPG's--they're not all the same--actually see the story as an important part of the game and take a lot of time to develop characters and let them interact with each other. A lot of people like that, and a lot of people don't.
Personally, the best games for me are usually ones with great experiences overall, e.g. gameplay, story, graphics/presentation (even games with outdated graphics like Earthbound can be presented very well in which case the graphics don't need to be ultra-realistic 3D models rendered in HD for me to appreciate the game), and last but not least, music. A lot of awesome games don't have the crazy detailed adventure "epicness" of JRPG story-telling so whenever I feel like getting some of that, JRPG's are the way to go.
That being said, games can still be amazing even without super intense or complicated plots. Call of Duty stories are usually solid enough to get you through the campaign (even if they don't shock you) and plenty of games are told in a way where they don't overflood you with text or details but still manage to get you invested in the story or riled up when there's some crazy plot twist. And some games like ones in the Legend of Zelda and Super Mario series don't impress me at all, and a lot of racing games have like, no story, similar to how fighting games' arcade modes are pretty much just a series of showdowns where tbh most people probably don't want to be bothered with a story anyway.
tl;dr IMO JRPGs are great if you want to grow attached to a game and want a little bit of everything (assuming you're playing a good one anyway). Music, gameplay, graphics, presentation, story, the only thing they usually lack is great multiplayer, haha, though that's not to say they don't ever have them but it's often local multiplayer and not a huge aspect of the game. XP