"A role-playing game (RPG) is a broad family of games in which players assume the roles of characters, or take control of one or more avatars, in a fictional, or real, setting. Actions taken within the game succeed or fail according to a formal system of rules and guidelines. Role-playing games also include video games in which players control a character or team who undertake quests, and whose capabilities advance using statistical mechanics. Despite this variety of forms, some game forms that are related to role-playing games may not be included. Role-playing activity may sometimes be present in such games, but it is not the primary focus."
-Wiki
I know I used Wikipedia but it was reliable and correct enough to get the point across. Plus anyways, its ridiculous to try to define that Mario Galaxy really has a story. I have never heard of a P-RPG before either.
I personally like:
Pokemon, if you consider that an RPG
Paper Mario, again, some may consider this not to be one
Final Fantasy XII, I really loved all the extra stuff
Chrono trigger
FF Tactics
If there are more, Ill think of them later. o: