Every once in a while, a tree bearing your town's native fruit will produce a perfect fruit. Your town also starts with one by default. I have cherries, and when I started out I sold the perfect cherry. I didn't know how rare it was until after I had given it to Reese...
I didn't get my second perfect cherry until a year later, and I locked it away for a month for safekeeping because I was scared of accidentally killing the tree, but I finally planted it and now I have a nice grove of perfect cherry trees.
Cool! I have all the regular fruits (including durians, lemons, mangoes, lychees, persimmons, coconuts, and bananas), perfect cherries, and a singular perfect peach and perfect apple.
I'm trying to collect the rest, though!
I didn't get my second perfect cherry until a year later, and I locked it away for a month for safekeeping because I was scared of accidentally killing the tree, but I finally planted it and now I have a nice grove of perfect cherry trees.
I'm trying to collect the rest, though!
http://animalcrossing.wikia.com/wiki/Trash?file=Rusted_Can.png
Just kidding