Before starting, I want to reiterate that every videogame can technically be called a "role playing game." Zelda, MGS, Mario, etc. I take the literal approach saying that any character in any game that we are using is a role that we assume. Now, I've tried to find a new term for the Japanese "RPGs", and I came up with "Anime Fantasy Adventures." Most games either wink at or borrow heavily from established anime cliche (or base the entire game around them). Final Fantasy tends to avoid it, but the genre as a whole sticks very heavily to the distinction I'm making. I'm not as familar to Western "RPGs," but those could still have a better genre title as well, or just fall into hackandslash/sandbox/shooters like everything else does. Anyway, here's my list of my favorites;
1. Persona 4
Enhanced Persona 3's addicting gameplay to incomparable levels
2. Final Fantasy VII
Until Persona came along, nothing could touch it. Building on VI's game mechanics, VII created a dystopian, realistic setting. Yes, the "brooding" and emotional baggage can get a little much, but it added to the experience. The game stands on its own as the biggest in the genre. Part of that is endless internet hype, but the game has too much going for it not to be deserving of praise. The game ages surpising well in spite of ugly character models, random encounters, and unskippable cutscenes (those last two should never exist in any game ever again).
3. Persona 3
Think of FFVII's emotional baggage, but mixing in dating sims and dungeon crawling
4. Final Fantasy X
Straightforward story and gameplay with the proper progression; everything built upon itself and the stakes grew along with the character's powers and relationships
5. Lufia II
I was pleased to see Zelda style platforming and puzzles integrated into what is normally a "grinding" video game. The remake did remedy the grind and flesh out the characters, so I appreciate that. It also didn't ape the story to a tee, choosing instead to alter the placement of characters, story arcs, and circumstances.