What really confuses me is when people use words that have a definition and use those words as they see fit. 1) The definition of role http://www.merriam-webster.com/dictionary/role. 2) The definition of role-play: to act out the role of OR to represent in action. 3) The definition of game http://www.merriam-webster.com/dictionary/game. So in summation a role-playing game (RPG) is a game in which you play the role of a character. So by definition it is a game where the player makes choices for the character he/she is assuming the role of. Now because most people "know" the definition of role playing game the first paragraph here may seem pompous but it serves a purpose. Now on to the examples.
Now Dungeons and Dragons is the first good example of a role playing game that is still around. In this game you create a character. You live out every decision of this character within the bounds of the game rules and the dungeon masters imagination. This is the closest to RPG you can get by its pure definition.
Now when you start talking about video games the developers only have so much leeway. It is impossible to make a game in which the character can make every decision of your character, have every setting, etc. With a game like Oblivion (without mods) you have a game with a permanent, unchanging setting. The laws of the world will always be the same not matter what the player does. A player cannot travel in the future and live an adventure there or to go into the past is also impossible. You also cant move through out the entire land, instead you are given boundaries that are made of invisible walls. Now with the addition of mods you are given even more leeway. The possibilities are almost endless but are never infinitely dynamic. The other games that fit into a category like this one are Mass Effect, the Fallout games, The Elder Scrolls games, etc.
Now onto Japanese RPGs (JRPGs). Final Fantasy VII is a disgrace to the RPG genre. You make no choices for your character except minimal choices like what dress Cloud will wear or what equipment each playable character will wear and even that is mostly made for you. At least in FFVII you choose your characters names. You don't role play ever in this game. FFVII is a turn and menu based game with cinematic making it almost like an interactive movie like the Halo series. I guess at least the Halo series calls the stuff in the middle of the cinematic first person shooting which is exactly what the game play actually consists of. The other games that fit in this category are every Final Fantasy game, every Dragon Warrior/Quest game, Xenosaga, etc.
In summation people often get really confused and say that games like Oblivion and Mass Effect are not RPGs, where games like Final Fantasy are RPGs. I hope that after reading this article you will no longer be confused about which is which. Thank you and have a great day.