I keep getting different answers, and none of them seem specific to Animal Crossing New Leaf, so I'm not sure if my villagers who move out will remember me or not. What determines it? I know that they'll remember you if they move to a friend's town, but what if they just move out? I'm getting really frustrated trying to find the answer since I've searched everywhere on the net and none answer my question.
It depends on how you meet the villager after they move out. If it's on your main street, then yes, but if you reset your town and then the villager moves into the new town then they won't. I had Jacques in my old town, then reset it, and he moved into that one and he had no idea who I was. If you see the villager that moved out in a friend's town they will remember you. It all depends on where you see the villager afterwards.