That happened to me once a long time ago. Usually it's either because I'm very lucky, or I have a good relationship with that villager. Sometimes I feel bad though considering they give me so much and never let me return the favor.
Yup, this happened to me with Pekoe. I really hate when they give me gifts because by gifts my animals usually mean things from their houses. LOL. I was playing at 6am I think, and Pekoe gave me quite the share of gifts. It only seems my animals want to give me gifts when the retails closed, and it's really inconvenient. Pekoe recently just gifted me an iron frame.
Phil and Tammy gave me lots of gifts when I had them. I had a high relationship with them though. My current villagers don't give as many gifts because I don't have the time to build relationships that high anymore.
I had it happen with Frita in a friends town....she kept on giving me pictures for the museum....the only problem was that they all turned out to be fakes.....but at least I did not pay her for them...
the best set of gifts I got was when Kiki first moved to town, she gave me a royal throne, a white katana, and a black katana, all in the same week; of course, i was bringing her perfect fruit, but still...