To add to what Raziek said of the ones he listed I'd definitively recommend Catherine, The World Ends With You, and Xenoblade. Like a lot of what he recommended was very good, but I want to emphasize those 3.
Catherine is a really good puzzle game with an interesting story. The music is fantastic and strangely fits with the whole thing. It is challenging and fantastic .It also has a really good 2-player mode.
The World Ends With You is an RPG where all battles are controlled through the touchscreen. You control a kid named Neku as he has to survive in the reaper's game for 7 days. To battle your enemies you are given psychs (in the form of pins) every pyschs has a different ability and you can equip a maximum of 6 of them, playing around with what type of combination you prefer is pretty fun in itself.
There are SO MANY DETAILS in this game that make the whole thing amazing, the way you grind stats is by eating food, and each character has a different set of food they prefer over the other, characters can get full after certain amount of "bytes" Every store has its own set of brand clothing, and combining the clothing of brands and pin affect the overworld and bonus stats you can get (plus you can also crossdress and its even encouraged as it gives big bonuses)
The story is pretty good, so are the characters and the OST. I heavily it recommend it if you haven't played it Circus.
Xenoblade is a long RPG with an interesting combat system and a likeable party. It has a huge world that you are basically free to explore after a certain early point in the story. The music is GREAT, every track fits the area really well, and the the battle music is phenomenal too.
I feel the story starts very strong, but falls short near endgame, its still enjoyable. The only big downside I'd say the game has is that most of the sidequest are very generic and poor, but the good thing is that you can stockpile accepted sidequests and clear them as you go along, its not necessary to go back to the person that requested it to clear it in most occasions.
You can chose to primarily control any member f your party, as the AI controls the other 2. You can chose whoever you think fits your playstyle best, and suit the party accordingly.
Quoting people from other forum.
Wonderful 101 is a game where "**** gets real exponentially, gameplay and story-wise."
or alternatively: " is just a series of events causing **** to get realer and realer until **** is at its realest."
Both descriptions also apply to Metal Gear Rising too.