Actually, there are quite a few RPGs which don't require pen and paper. Also, Bioware games and the Fallout series are good examples of actual roleplaying in video games.

@richardhutnik

i don't mean to be offensive but, i feel GoW, and DMC redifine the quality of the genre. comparing these two to RPG games make me feel that its nothing special when it actually is mind blowinly awesome.
JRPG games are lacking quality wise nowdays. i blame square for releasing half assed JRPGs. WRPGs are a total different thing though.
I think GoW deserves its own genre of "over the top awesome badass action which is brutal" (OTTABAWIB)

With videogames, it is entirely possible for a game to borrow all over, and be something unique.  Because of this, I didn't want to get into a debate into what God of War is, but rather, what is a role-playing game.  God of War sits right on the edge of RPGing.  I was going through older PS2 games I have, that I never got to, and have been playing God of War, and saw the leveling and thought, "This could be argued to be an RPG", eventhough the game isn't positioned and marketed as such, the way the likes of Diablo is.

The thought also recently occurred to me that a lot of videogaming people do is closer to being what a role-playing experience is actually meant to be, than what gets marketed as computer role-playing games.  In them, you actually play a role, and live as an alter-ego.  I also thought that Call of Duty 4 has mechanics normally associated with RPGing in the multiplayer: gain experience and level up your skills.

As things go on, more blending will likely happen.  Adventure games, for example, have fused with action titles, to make a genre called action-adventure, and then these had ended up just dropping the adventure part.  Way back when adventure games used to be purely text based things, where you typed in commands.  Then Sierra and LucasArts (back then LucasFilms) came along and made them strictly graphics based, and point-and-click.  Then, the arcade games became action games, and started incorporating adventure elements into them.  Even the likes of Doom, with keycards, fit this.  You dealt with puzzles, but had to do action sequences.  I know Half-Life (the originally) made me think adventure games with with what it had.

So, now we are at, what the heck is an RPG?  This is particularly true with games like God of War, which happens to have you playing Kratos and pumping up his stats, and online FPS games adding stat-building and roles you play.    

RPG's involve playing the role as you see fit by making decisions. These decisions include what dialog options to use, missions to take, skills to acquire, alligience to take, etc... God of War is far too linear to qualify as a true RPG.

I tend to take the same stance, but that's also generally true of most games that are labeled as RPGs, especially JRPGs, going all the way back to Final Fantasy I.

RPGs are games in which you define your character and decide what they do. There may be a path for you to walk, but you can choose whether or not you can walk it. Bethesda is one of the only companies right now still making true RPGs. BioWare does too, ut it's to a lesser extent of late.