Getcomposted: Okay, RPG's seem to encompass a lot of types of games right now. Here are a few, not all, of them.
There's the ARPG (Action RPG) where you run around hacking 'n' slashing. With every kill you gain EXP to level up. A good example of this, imo, is Divine Divinity. You get an open world to quest in and the fights are more or less real time. A lot of mouse clicking is needed especially if you venture into an area past your level.
Then there's the dungeon crawler - Legend of Grimrock, Eye of the Beholder for first person views, or the Avernum or Avadon series for a top down or isometric view. These tend to be turn-based with lots of wandering around mapping places. A quarter exploration, a quarter survivalism, a quarter puzzling (because
obviously, you need to find the stone idol's ruby eyes to open the door), and a quarter fighting.
The SRPG (Strategy RPG), you command a team of heroes/grunts/ fighters that must defeat a group of enemies. You have to take into account variables like terrain, type of fighter, speed of movement, weaknesses and strengths against various types of enemies. Rock, meet scissors, not paper. These types of games are less open world and more series of battles culminating in a grand style, last gasp hurrah, this is for all the marbles, boss battle. Disgaea, Fire Emblem.
The JRPG (Japanese RPG) with the Final Fantasy series being a rather famous example. Spiky haired pretty boys taking on the ecological monster with improbably gigantic swords. Open worlds, random encounters, some kind of disasters destroying the world in some non-green fashion. An aspect of Japanese life is Shinto, a belief system that everything has an essence from rocks to trees to animals to people. If things are out of balance, bad things happen. Cue spiky haired hero with possible orphan or abandonment issues to come and find his destiny and save the day. Also big eyes.
And then there's the CRPG (Computer RPG) typified in the games of yesteryore like Planescape: Torment or Baldur's Gate. Here I think the genres are a little mixed as they tend to be the progenitor of all the tropes. Squad based, solo characters, they all jump in there. Usually turn-based, the plot lines are more westernized, think Lord of the Rings Big Bads rather than Sephiroth with mother issues. It's not a journey to discover yourself and your destiny, more a discover and investigate danger. Although Planescape: Torment is a discover your identity and purpose, just... not... Japanese. It feels to me like the character takes his amnesia in his stride. Yes, he'd love to find out who he is, but it's not going to stop him kicking ass and chewing bubblegum.
Anyway, my rather sleep deprived ramble on RPG's. There are so many types with so many elements that originate from RPG's spliced in the DNA of all genres of games now, I can't say that RPG's are at all niche. Maybe the very strictest of codifying what a RPG is would make them niche - toss out ARPG's as not being turn-based etc., but essentially, a Role Playing Game is exactly that, a game in which you play a role, and isn't that a description you could apply to most games?
[Edit: typos.]
Some definitions and other eploanations I don't agree with here.
First, the ARPG category. I actually don't consider them RPGs in the first place (they're action games that happen to borrow heavily from the RPG genre, but are still action games at their core), but regardless, there are many games that fit that character that don't require much mouse clicking. In fact, many such games that fit your definition are on platforms that don't even support a mouse in the first place (like the NES)!
Second, I wouldn't lump the games you call dungeon crawlers all in the same category. In particular, Avernum and Avadon do not seem like dungeon crawlers to me, and it seems that Wizardry-likes (like Etrian Odyssey and Elminage Gothic) ought to fit in this category.
Finally, CRPG is not a distinct category here; reading your description, it sounds like you are describing WRPGs (Western RPGs) with your description. CRPG, to me, refers to any RPG that is played on a computer (or computing device), and in particular, does include JRPGs as well as WRPGs. (This is a mistake that a lot of people seem to be making in this thread.)
One other thing: "With every kill you gain EXP to level up" is not a criterion that makes a game an RPG, nor is is a universal criterion that every RPG satisfies. The SaGa series (which is interesting in many respects, like the way it blurs the line between WRPG and SRPG) is a good example here; excluding the original SaGa 3, there are no experience points or levels, but instead you have different rules for character growth. Another good example is the Elder Scrolls series (excluding Arena); there are levels and something that counts as experience points, but killing enemies isn't how you earn them.
Getcomposted: I define an ARPG as a game whereby you have to fight in real time, and the speed at which you fight is predicated on the speed of your mouse clicks!
Why do you think the aspect of mouse clicks matters as far as genre definitions are concerned? If one wants an ARPG category, games like Crystalis and Final Fantasy Adventure ought to count, and neither game has mouse clicks; in fact, neither game was released on a platform that even supports a mouse in the first place!
Another problem with that definition: depending on how one defines "fight", your definition risks accidentally including Cookie Clicker and similar games, which I don't think was the intent.