Red Dead Redemption may be one of the best RPGs to come out this year.
Stop and think about it for a minute. When it comes to creating a place that feels legitimate and tangible, it's pretty hard to argue with New Austin's expanse. And RDR certainly has characters and dialog in spades (no poker pun intended).
If you really consider it, what differentiates an "RPG" from another kind of game? In days long past, when we were measuring Final Fantasy against Contra, having a large, free-roaming world was a novel and unique feature. Obviously that's no longer the case. Sandbox games may have actually surpassed the majority of RPGs in presenting a large, freely navigable continuous space.
Similarly, nearly all AAA single-player games are character-driven now. It used to be that the only RPGs contained characters that would speak to each other in nothing but the most cursory of fashions. Again, those days are long past. While the stories might not always have been well-crafted, they're certainly prominent in nearly all big-budget titles. Even the notion of player choice (nearly always good vs. evil) has been used in all manner of games.
With world and story no longer domain of the RPG, what remains are mechanical distinctions. The most prominent mechanics, i.e. level, hit points, etc., were inherited from tabletop RPGs. Stat-modifying equipment is a natural consequence of this, but not really a distinct feature by itself. Some RPGs have focused intensely on this portion of the genre, most notably Diablo and its more modern offpsring, Torchlight. Of course, as is evidenced by Modern Warfare (and seemingly every other yet-to-be-released shooter), experience and levels is a system that can easily be co-opted by other genres.
Another large distinction is being able to control a party of characters, rather than just a single one. However, we have seen this diminish as of late (especially in western RPGs) from having full, symmetric control of all the characters to embodying a single character and directing AI companions. Some recent RPGs, like Alpha Protocol and Demon's Souls offer no companions at all.
Having a robust dialog system with many conversation options is part of the western RPG tradition, but rare in Japanese RPGs, so this may only count for half. This quality is shared with adventure games as well.
There is something of a question of content and setting, given that many RPGs skew toward wizards-and-orcs style fantasy. I'd consider this also a result of their tabletop heritage rather than anything intrinsic, especially when some of the best RPGs around explore different territory.
With all that boiled away, what then is the difference between Fallout 3 and Red Dead Redemption? Is it just statistics and a dialog tree? I think there is one final difference, also inherited from the tabletop ancestry, that's most important: classes. While their specific implementation may vary, the high-level goal of providing distinct playstyles is pretty fundamental to the RPG. The classes may be spread amongst characters (in Japanese RPGs) or a choice offered to the player, but they're almost always there.
I'd say this is really the heart of the RPGs. Playing Red Dead Redemption, the player is always John Marston. When you're placed in a situation where you have to shoot, you shoot. When told to race, you race. When told to mosey and rustle, well, you get the picture. The player has very little choice in how to address a situation. Even with the greater freedom afforded in a game like Just Cause 2, sooner or later, you're going to be blowing things up. It's just a question of whether or not to buy two grenade launchers or steal a helicopter.
I'm not convinced that the low-level mechanical trappings of RPGs are what make them interesting and special. I don't think Morrowind or Arcanum would be poorer games if they didn't have levels. In a single player game, the notion of level is largely illusory anyway (and in the case of Oblivion, barely an illusion). The numbers get bigger, but the game rarely becomes radically more difficult as you advance in level. It works at conveying a sense of progress, but there are other ways to do this. But the choice afford by the best of RPGs is unparalleled.
Are we going to see a convergence of RPGs and sandbox games? Perhaps. Take away the leveling and we're more than halfway there, I'd say. Imagine a game with the playstyle freedom of Deus Ex and the grand, sprawling world of Just Cause 2. Sandbox games with rich, emergent worlds succeed in providing small moments unique to each player. Great RPGs offer the ability to make large scale decisions that fundamentally alter how the player approaches the game. Putting those things together would be quite the challenge, but the payoff would be astounding.
I'm not sure who would make that game, but I cannot dispute that I would play the everliving hell out of it.