Unicorns date back to at least the Greeks (in terms of people thinking it was a real creature, at least), but for a time in medieval Europe the discovery of narwhal horns washed up on foreign shores kept belief alive for a time.
Hodag (North America)
It's rare that the mention of an investigation is enough to kill a cryptic, but that's the case with the hodag. A hodgepodge of parts (frog head, elephant face, reptilian body, and massive claws), prankster Eugene Shepard seemingly concocted the hoax to make a profit displaying it to the public, but as news spread across the country and scientists expressed interest, he was quick to reveal the hoax.
Hoop Snake (North America)
Sightings of this creature go back to at least the 1700s and continue to this day. People claim the snake is able to bite its own tale and roll after its prey like a wheel, with some adding that it can unwind at the last moment and spear its target. It's possible that people are confusing it for snakes that mistakenly attack their own tails, though that wouldn't explain the wheel-like movement.
Hotheaded Naked Ice Borer (Antarctica)
Discover magazine ran a piece on this non-existent animal in its April 1995 issue as a joke, using photo-manipulation to create what appears to be a horned naked-mole rat. Though the magazine included clues that it was a hoax (and accompanied the piece with other prank articles), the hoax persisted for a time as outlets like Ripley's Believe it Or Not (knowingly or unknowingly) reported it as true.
Furry Trout (Various)
The fur-covered trout was alleged (at least in North American telling) to had evolved to grow fur due to the cold waters it inhabited, and in some versions the fur comes off completely when it is brought out of the water due to sudden temperature change. There may technically be some truth to the existence of this creature: a fish infected with cotton mold could appear to be furry.