REBUTTAL TO: Really, I'm an RPG!
There are some games that just aren't. Sure, you can find them in a game store, but you can find strategy guides in game stores, too; that doesn't make them games (well, it might be a game if you enjoy trying to figure out why the guide gives you two different locations for the same thing; northwest or northeast, which is it, people?). There are "games" that are applications. The upcoming Jam Sessions for the DS is one such "game." Mario Paint for the SNES was another example of an application masquerading as a "game."
The type of non-game I want to discuss here, however, can be called the "Second Life" phenomena. Sony's new initiative, Home, is just one example. The Sims, Nintendogs, and, yes, Animal Crossing all fall into this category. These are games that never end. Ever. There is no final boss. There is no princess to rescue. You have no goal other than the ones you set for yourself. They are virtual worlds, and, just as the real world is largely unscripted and infinitely continuous, so too are these games. In three out of the four examples I gave, the world continues to evolve and change even when you're not in it.
To be fair, Animal Crossing does present players with a number of pseudo-goals to achieve, but none are forced upon the player. You can interact with your fellow townsanimals and beautify the town to attract more potential friends. If you ignore your neighbors and allow your town to degenerate into a weed-infested wilderness, however, there is no "Game Over" screen. Your character never dies or ages. You never have to actually make a payment on your mortgage, provided you're happy with the current size of your home. There's certainly not a linear path to finish the game; neither is there an open-ended path to finish the game, since there is no game and nothing to finish.
The only personal growth your character experiences is the materialistic accumulation of a larger home (always accompanied by a larger mortgage), more furniture and items with which to fill said home, and a large pile of bells, the currency of Animal Crossing. The only "story" to be told is the story of your own personal hatred of Tom Nook, demigod of your Animal Crossing town.
I played Animal Crossing every single day for months; I then took a four-month hiatus (for which the few remaining townsanimals berated me endlessly, but I suffered no other ill consequences). Since picking it back up, I have played it, again, every single day. I ignore my fellow townsanimals as much as possible. I haven't caught a fish or a bug in months. The only town beautification I engage in is the planting of "foreign" fruit trees, whose fruit nets me 500 bells apiece, versus 100 bells for "native" fruit. In short, all of the normal, prosaic goals of the game have been thrust aside in my avaricious pursuit of more bells. I even go so far as to schedule real life activities around the game so that I can properly play the stalk market.
Is it role-playing? Maybe. I'm certainly not a capitalistic tycoon in real life, nor do I want to be. Is it a game? That's even more doubtful. Is it an RPG? No. It has some RPG elements, true, but so do games like Crackdown and Ratchet & Clank. The collection aspect, the presence of interactive NPCs, even the buying and selling of goods, have all appeared in various RPGs, but they do not an RPG make, nor are they RPG-exclusive elements. There is no story. There is no character progression, either in personality development or in stats. There is no battle system, no EXP, no HP, no MP, no equipable weapons or armor. There is no final boss, no dungeons, no exploration, and no end to this game. The online aspects of it might bring it closer (though only marginally) to MMORPG status, if there were some sort of lobby through which to access players' towns. No such system exists; the only way to visit another person's town is to get their friend code. Still, even with such an addition, the online game would be little more than a massive simulated economy.
Will the standard player of RPGs enjoy Animal Crossing? Absolutely, though it's not an RPG. Animal Crossing is simply the sort of open-ended non-game that anyone would enjoy.