In my opinion, what counts as a RPG is subjective, not objective. If you feel like you are the character that you are controlling, that you are in their role, then subjectively, that game is an RPG for you. Though to call a game an RPG objectively, I'd say you need to be able to choose what to do, what to say, and the choice you make makes a significant impact on the game. By significant, I mean something from changing the ending, to changing what factions like you, to shooting a guy so you can loot his cowboy hat.
OT: WRPG, I'd say oblivion, though i haven't played many RPGs really, ME, ME2 and Dragon age I'm getting when my exams end. oblivion has many flaws, but the music still doesn't get old even playing for so many dozens of hours, its aesthetically pleasing, and I can make my own back-story and choose how to forge my path, and the combat isn't great, but its not bad either and is good enough not to break immersion. despite all its bugs and levelling system problems and oblivion gates, no other game has kept me immersed as well as oblivion, and that what counts over all for me for an RPG.
JRPG, I would say Mother 3. Because i distinctively dislike turn based games, thus most JRPGs. but mother 3 was funny, had a good story, had lovely music, and the way you could combo to the music was awesome, too bad emulators make this hard. and I'm too terrible a gamer to play mother 2. FFX though would be a close runner up. it is the only Turn based game I like, I think it is perfect combat wise. It's tactical and fun. but as aforementioned, I'm terrible at games and got stuck.