Dōbutsu no Mori for Nintendo 64, though even the first AC for GameCube is significantly improved such that no one is likely to care except perhaps N64 enthusiasts.
A more straight example is the third release in Japan, Doubutsu no Mori e+ for the Gamecube. It only saw a release in Japan, and many of the new features that it introduced that were not in the N64 and U.S. and European release haven't been used in future titles in the series (such as hitting Nook's store door with a shovel when he's closed and being able to shop after hours with Nook half asleep and the prices for stuff being inflated when you do this). However, a select few of its features have made it into future titles in international releases (such as being able to eavesdrop on animal villager conversations and them asking you stuff during them) making them first introduced to Western audiences in the Wild World and City Folk releases.
Want to cuddle with a plush of your favorite Animal Crossing character and you live outside Japan? Be prepared to part with a lot of cash to have them imported. The US did get some during the Wild World era, but production/importation of the toys for the US market seem to have ceased since.
Villagers that only appeared in the original Doubutsu no Mori and its GameCube updates.
Nintendo Zone exclusive DLCs. If you live in a country where there are no Nintendo Zones, you're shafted. Similarly, region-specific DLC items (such as New Leaf's Japan-only 7-11 set) or items associated with region specific holidays (e.g., the Labor Day picnic basket in the North American version); however, if you're lucky, you might be able to find someone from the region who's willing to trade with you online.
Science Marches On: Seismosaurus is one of the dinosaurs the player can dig up in the second and third game, even though that turned out to be a dubious genus and instead a species of Diplodocus. The fourth game, however, managed to acknowledge this and renamed it Diplodocus.
Sequel First: The N64's Animal Forest never left Japan, while the GCN's Animal Crossing was the series's international debut. But the GCN game isn't exactly a "sequel" in the sense that the DS game is a sequel to the GCN game.
There was an unused character in the first game, presumably a special character since her clothing doesn't change (that could be due to coding though) along with a sickle item. The sickle's removal could probably be explained by the fact that its use would be cutting smaller (i.e. excluding non-sapling trees) plants (e.g. weeds, flowers, or saplings), but in the final game digging them up is possible so having two tools to get rid of weeds, flowers, or saplings would be redundant, especially since weeds can be removed more quickly without a tool (though since picking flowers wasn't possible until later games, digging up flowers is the only way to get rid of them) and dead saplings disappear the next day if they aren't dug up manually.
An Animal Crossing 2 was announced years ago for the Gamecube but was eventually cancelled.