This one is tricky, because most animals do learn and thus can be taught certain behaviors or activities. What we're talking about is not just observation and imitation, but an animal actively trying to correct and intervene. There's a study that shows that chimps, for instance, don't correct a younger chimp who is incorrectly trying to crack a nut. Instead, the younger chimp must just learn by trial and error [source: Zimmer].
But there are a few examples of animals actively showing "method" in teaching. One is the meerkat, a species that includes scorpions as part of their diet. Instead of teaching their young ones by letting them loose to try their hand (a dangerous activity for those without experience), they bring back dead or nearly dead scorpions for "practice." As the pups get better at racking up fatalities, the parents bring back scorpions that get progressively livelier, until the younger ones are skilled enough to hunt themselves.
Even more sly are elephants who teach their kiddos. A young fertile female might shy away from the advances of a strong bull -- a mistake for both protection and procreation. An older female will fake being fertile, and cuddle up to the bull. The young female will see the error of her ways, and approach the bull herself.