What game impressed you most with its character depth and story development?

I literally got blacklisted for this more than for a racist joke I made few days ago XD

As a genre label, no- the label most typically applies to anything with a leveling system, these days. Past that, even actual character-role-filling examples of the genre are dominated by the shallow offerings of most MMORPGs, Bethesda games, Hack'n'slashes, Diablo-likes, generic JRPGs, and so forth.

While RPGs often do have at least a simplistic story offering (which, say, platformers rarely give even that much attention to), they rarely even come CLOSE to the depth of story present in better Visual Novels and Adventure games. I mean, point'n'click also covers Myst-likes and puzzle PnCs, so it's not like the genre doesn't have its own shallow offerings, and VNs have so many low tier Sakura-esque offerings that've been pushed into prominence that most people don't even see past the stigma that thin layer casts upon the genre; nevertheless, both genres are still associated with offering richer stories, when the emphasis of the games is toward story-telling (and that's an impression which Cinematic Adventure games like Telltale games and Life is Strange have only further emphasized among modern gamers).

Rather, other than Black Isle/Troika/Obsidian (Keep in mind, that's all technically just a single team designation- Interplay originally created Fallout 1, and the team involved in that split up into Black Isle and Troika. Black Isle reformed into Obsidian, and reabsorbed Troika as that studio dissolved.) and Bioware games, it's difficult [though admittedly not impossible] to find any western RPGs that actually dedicate themselves to storytelling or atmosphere. JRPGs have quite a few more RPGs which easily stand out, but that may just be because there are so many JRPGs out there- the overall percentage of JRPGs which stand out for their narrative is still very small.

Of course, I can put the perspective into a more simple framework:
It's a heck of a lot easier to find the story-rich VNs and adventure games, since there are so many of them, and the hobbyists for those genres tend to emphasize and highlight those games. Likewise, gamers less enamored with the adventure genre also emphasize story-rich (but also accessible) examples of the genre as standing out.
With RPGs, gameplay often gets more emphasis than story, both in what developers and gamers focus on, meaning it's harder to sift out the story-rich RPGs.

Well, regardless of all of what I've said above, only one truth really bears relevance on this thread:
I, personally, have absolutely no trouble finding story-rich adventure and VN games, but do find it challenging to find story-rich games in any other genre, outside of the offerings of a few specific companies known for focusing on such.
As such, a thread like this has a lot of potential value for me- while a thread covering adventure games and VNs would be mostly (or perhaps even entirely) redundant to the knowledge I already have. Hence it made sense to trim down the answers to the ones most useful to me.

Besides, story in genres where it's unusual makes for more interesting discussion, and past that, I've gotten a lot of interesting answers with this thread- ones which I may not have gotten if I'd left it less specific. :)

Huh. Didn't know Hiro had a game.