Ok I decided to do this while trying to choose a game to play this morning and I thought I'd give out a list of Must Have JRPGs and my reasoning for them. Here is no particular order of preference of my choices as must haves,
Lost Odyssey is a great game with a must experience story. It's combat system is considered dated, but the likable characters and touching story will keep you grinding though the battles until you reach the epic conclusion of the game. Admittedly the game is about 60-80 hours long unless you grind your stupid to max level. This is my favorite JRPG too so you know it's got to be good!
As a Final Fantasy fanboy I'm obligated to mention this game as a recommendation, but I do like Final Fantasy XIII. It's story is well written and most of the characters grow on you (except Vanille) and it's revamped battled system adds a unique flavour to the game. Admittedly the crystarium is annoying because of being limited to how much you can level up on it during the progression of the game.
This underrated game is the best looking JRPG released to date and has a beautiful musical score. The story of Eternal Sonata is intriguing and enjoyable and I also think it was wrongly classified by the OFLC. I would recommend the PS3 version over the 360 version for the extras in the game and this game is so good I own both version of the game. If you miss this one then your missing out on a great game.
Another entry in the Tales series that anyone who's ever played a Tales game should already own. Tales of Vesperia has a great story and combat system that keep this game going and makes it hard to want to put the game down. The game's story is one of the best in the Tales series and the replayability in the game makes it worth playing though multiple times.
To be honest I'd love to recommend all of the JRPGs available outside of MagnaCarta 2 but I'm sticking with the cream of the crop and these games are the best one out at the moment. I recommend these to those who have never played JRPGs because all of these are great and JRPG fans should already own these games.