Three notable games of mention for me.
The first is The World Ends With You. I was browsing some Kingdom Hearts fansites at the time, and occasionally they would report on the game because Tetsuya Nomura, who works on the Kingdom Hearts franchise, also worked in this game as well. But I didn't think much of it, and aside from compliments of the music, everything about the game was in the background and I knew nothing. Fastforward a few months later, and I end up going to Gamestop and seeing TWEWY there, and its the last copy. I wanted to buy something, and nothing was really grabbing my attention, so I said "What the hell, its the last copy".
Ended up being one of my favorite games of all time. The music was indeed great, the battle system was fun and required some time to master, and the characters felt great. But most of all, the game was hilarious, and even it's side chapter was just a nonstop rollercoaster of laughs. Even better though, is that I actually WANTED to try and get as close to 100% completion in an RPG, which really doesn't happen to me often (just side dungeons, bosses, the basic stuff). Got around 93% complete, and I had fun the whole way.
The second is Nier. I remember browsing through Kotaku and occasionally the game would come up during pre-release. Mostly it stemmed from one character in the game that looked like a girl, actually being a boy (or some gender/genital revealing fact). I remember there being a few more articles about the game, where they were trying to clarify exactly WHAT the character was (which is slightly more complicated in the actual game). That was pretty much all I knew about it except for some type of sickness that was apparently a focal point of the game. So the game comes out, and around Christmas time as I'm putting my list together, I trying really hard to get some RPG's I want. Remembering Nier, I decided to just put it on there as one of my last items and if I didn't get it, it was fine.
Holy crap did I love this game. The music was AMAZING (almost all of it felt like it had some lyrics to it), the voice acting was really good, the story was depressing (even moreso on New Game+ where they add additional story cutscenes to make you feel horrible), and I found the lighting effects to really strike a cord with me for some reason. Nier was another game that made me really want to try and get 100% completion (or at the very least most of the trophies). Just settled for getting all of the endings.
This tends to happen with me and RPGs. Most of them are random buys and I barely know about them. These two though are my go to ones, but there are a lot more (Xenosaga series, Star Ocean 3, Fire Emblem series, Tales of Xillia, Golden Sun, just to name a few).