Final Fantasy-less title: Shadow Hearts Covenant
Totally Square-free developer: Sacnoth/Nautilus
Why you should ignore Rikku and play this: Because it's basically a funnier, gothier, quirkier version of Final Fantasy X. You've got your sassy, anime-styled badass hero, your sexy babes, and your strange magicians. You've got summonable monsters - in this case, demon forms that the main character can literally become. And you've got your three-member battle party and a turn-based battle system that they use to keep a bad guy from royally effing up the whole planet.
You also have a level of comedy and just plain randomness absent in most other games. One of your characters is a buff, vampiric wrestler who wears a butterfly mask and clobbers enemies with a locker or mailbox. Another is a wolf who spews awesomely cheesy smack talk at other wolves you meet, and then fights them. A third party member is a magical old puppeteer with a disturbingly realistic magic little girl marionette - for whom you get new clothes (and therefore spells) by finding gay porn and trading it to a certain merchant. We're not making this up. And it's all awesome.
Plus, many people at developer Nautilus (formerly Sacnoth) had actually worked for Square in the past, so they knew how to make a quality RPG. It's still a PS2 game, but Shadow Hearts Covenant looks great and boasts motion-captured cut scenes, decent voice acting, some gorgeous CG moments, and a moving ending that stays with you for a long, long time. It's also the second game in a series of three, so if you dig this, grab the just slightly weaker first and third entries as well.