RPG's: Xenogears, Xenosaga, FF series(XIII included, sue me) except a few(X-2, stupid spinoffs etc..), Chrono Cross, Soul Sacrifice, The world ends with you, Breath of Fire 3 and Panzer Dragoon Saga.
Non Rpg's: Bioshock, Last of Us, VLR, 999, Phoenix Wright games(Goofyness is not incompatible with maturity imo), MGS series.
"Non sensical" plot has nothing to do with Maturity for me, I want characters that behave like human, even if they are unlikeable, I just want their behaviour to be consistent and indicative of their personality and to be believable to the situation at hand, they dont need to exactly do the right thing or the most logical thing(emotional state affects our rationale considerably), they just need to have a believable behaviour. I think people underestimate RPG characters and just put some stupid label devoid of analytical substance on them like whiny or Melodramatic or whatever, if you really think about their actual circumstances and if you tried to put yourself in their shoes in a universe with rules like theirs, most people would run away like cowards or shit their pants on the spot. I like characters that start out very flawed that are forced to grow up through the shit hand they have been dealt. To me a mature plot, is a plot that makes me think and that has some complexity and depth to it, a plot that generates discussion and sparks the imagination of the player, it's not about "maturity" in the traditional sense, plots with characters that mature throughout the story are just as good as the ones that start out with already mature characters, if done right of course. So I guess I relate maturity to complexity, convolutedness in a positive manner, believable characters and a deep narrative.
I reckon not many people will relate to my definition of maturity buttfuckit, it's the way I see things personally.