The always well researched Brian Switek of Laelaps has a couple of excellent pieces up about now-extinct megafauna and those who believed there might still be some around. The first deals with a tall tale told in the 1890s of a mammoth hunt.
The picture above is of a mastodon (Mammut) not a mammoth (Mammuthus) but still I'm out of mammoth pictures so you'll have to make do with a different yank pleistocene prosbocidean. The image below is from San Diego's Natural History Museum and is of Harlan's ground sloth as Brian's second tale is of a group of scientists who mistakenly believed giant sloths to be walking the Argentine pampas and disembowling people.
The odd cryptozoologist still suggest these animals survive in South America as the mapinguary but I'm going with those who suggest the footprints referred to actually belong to unknown populations of Giant Anteaters. Of course we certainly shouldn't mock those in the days of exploration of the new world believed the creatures might live on, there was no reason to suspect they didn't and if they did, well, wouldn't that just be the coolest thing ever?