Is this a new feature? It was not in AC:WW so I was really surprised when Avery knocked on my door unannounced, while I was in another room trying to furnish it!
I let him in and he gave me a present! He stayed a while, we talked, then he left. This is so awesome. I believe my relationship with Avery is higher than with any other villager in my town, maybe that's why he could visit me without an invitation? I have yet to receive his picture though.
Peanut completely surprised me today, and it was a very pleasant surprise... she gave me my first persimmon! Totally mailing her some awesome furniture now!
Rocco. I think he has visited me twice? I've been visited twice, that much I know. And since I can't remember who else, it was probably Rocco both times. It kind of scared me the first time, because I didn't know that they would randomly come over in NL
Recently, Bunnie has been dropping in unannounced whenever I finish organizing my storage. Most of the villagers who I regularly talk to come over to visit. At least they give presents the day after!
Frita barged in one day when redecorating my mainroom. Was a surprise at the moment but it was bound to happen as I have highest friendship with her than my other townies. And she's given me her pic.
Flora barged in moments after giving me her pic (and she gave me her pic while freaking out about how much I had talked to her that day ("I see you so much, you must have clones!")). Someone else in that town has also come in unannounced, and I'm pretty sure it was Mallary.