Would work well with: The World Ends With You, which actually does include rap as part of its soundtrack. However, since the game takes place in an urban area, the main characters are all teenagers and the rap songs aren't used in Shiki's chapter, it fits the game well.
Would work badly with: Most RPGs. They take place in semi-medieval or futuristic settings, where modern rap music would just tear you out of that world and remind you that it isn't real.
I'd be ok if they had several different choices for music for battles and such. I don't like rap much but occasionally theres a really good song. Unfortunately for the industry, most of rap is people talking about where they came from, what their vices are, and about how they have really "deep" things to tell the world.
Currently playing: WoW Private server (Warsong 12x) - https://www.wow-one.com/ -- Xbox Live Gamertag: RevenanceSLC
Eh... Only if it's good like the Beastie Boys. Though I really can't imagine any sort of JRPG having rap music.
Otherwise, I'd have to go with computer generated music and symphonic music. Some games could also do with some classic rock/punk (or maybe some newer stuff, though I'd be reluctant to put something like Green Day in any games), though I'm not so delusional to believe that JRPG's and hardcore punk would go well together. Then again, what you think should be in games is completely dependent on your taste in music. If I were to be put in charge of the soundtrack of any given game, most people from the newest generation (Generation Z, or all those born in around the 2000's) would probably be turned off by it; my tastes more follow those of the previous generation (for which I am a bit glad, because I really hate the fans of Justin Beiber and other pop culture icons of this day).
What determines whether a game is good is your experience every time you play the game, not the opinions of other people (unless you let it do so).