There are actually several tricksters in Native American lore, with Coyote being the most significant in the Great Plains and parts of the Pacific coast. The Raven is also a major trickster character in the Pacific Northwest in particular, with deeds like the creation of Multnomah Falls sometimes attributed to either one in different Wasco stories. I've seen other myths with the Rabbit as a trickster, and even one with a crafty Sandpiper. Coyote seems to be the best known character in Native American mythology, though. His character can be quite different from one myth to another, but he's often shown to be a shape-shifter, and to have had powers to alter geography. He's been credited with slaying monsters (sometimes from inside their bodies), creating mankind, bringing fire to humans, and inadvertently making death permanent. For a trickster, he's sometimes shown to be quite easily tricked himself, and not unlikely to make a fool of himself.
One of the nastier tricksters in classical mythology is Loki, a giant who joined the Norse pantheon at the invitation of his friend Odin. Some myths show Loki as a willing helper of the Aesir, as when he helps Thor to retrieve his lost hammer, and accompanies him to the land of the giants. Others, however, have him trying to spread discord among the gods, and I have to suspect that he might just be someone who takes whichever side would be more fun for him. The last straw as far as the Aesir are concerned is when he is responsible for the death of Odin's son Baldur. As punishment for this, Loki is bound with his son's entrails under a poisonous snake. His wife Sigyn manages to catch most of the snake's venom in a bowl, but when she empties the vessel, the poison drips down onto Loki and makes him cause earthquakes. The story has it that he will remain bound until the time of Ragnarok, during which he will fight against the gods and end up dying. Like Coyote, Loki is a shape-shifter, sometimes even taking female form, and once becoming pregnant with a foal after turning into a mare in order to distract a stallion.
In Western Africa mythology, the most prominent trickster character is Anansi, a god who is sometimes portrayed as a spider, and has a lot of the same traits as tricksters in other cultures. One of the most significant Anansi tales involves his capturing various dangerous animals in order to purchase the very concept of stories from his father Nyame, god of the sky. The story of Brer Rabbit and the tar baby is thought to have originated as an Anansi story in which the god himself ends up being tricked. In Neil Gaiman's American Gods, Anansi (who goes by the name "Mr. Nancy" while in the United States) plays a major role, and relates a particularly smutty story about his stealing large testicles from a tiger.
Greco-Roman mythology has several figures who fit the trickster model. Perhaps the best choice would be Prometheus, whose role is somewhat similar to that of Loki in Norse mythology. Like Loki, he was a member of an enemy tribe (in this case the Titans instead of the giants) who defected and helped out the gods, but also went against them in some significant situations. The two most important are both occasions of his helping out mankind at the expense of the Olympians, once tricking Zeus into not taking the best meat in sacrifices, and another time stealing fire for humans (as Coyote is also said to have done). As punishment, he was chained to a rock, and a vulture would eat his liver (which, seeing as how its bearer was immortal, would automatically regenerate) every day; but he was eventually freed by Hercules. As my fellow Terry Pratchett fans probably know, Discworld had its own version of that myth, with Fingers-Mazda as the thief of fire and Cohen the Barbarian as the hero who rescues him from bondage. But getting back to the actual Prometheus, unlike with the other tricksters I've mentioned, I don't know any stories of his ever becoming the butt of the joke. That role might, however, be fulfilled by his slow-witted brother Epimetheus, through whom Zeus punishes all mankind by means of Pandora and her box (which was probably actually a jar). Hermes is also sometimes portrayed as a trickster (as, for instance, when he stole Apollo's cattle during his childhood), while Loki's role of sowing discord is attributed to Eris.