I was very surprised to find how few people knew of these animals...especially since they live in my country. Peccaries, or javelinas as they are sometimes called over here in the states (though javelina may be used just to refer to the Collared Peccary, just FYI), are not pigs, but actually a group of native North American mammals, some of the few to survive the extinctions of the Late Miocene (the other survivors? Pronghorn, canids...and I think that's about it. All the rest are extirpitated or extinct). Unlike their pig look-alikes, Peccaries have wicked canine teeth, which are built more like fangs than tusks. There are three (possibly four) species of peccaries, and what makes them interesting is that they have been able to adapt to habitats in North America that pigs cannot. Also some evidence suggests that the peccary's closest relatives...might be entelodonts. Chew on that for a while.
2. Tree Shrews
No, despite the name, these are not shrews. In fact, if one were to put them in any already existing order, one might as well call them primitive primates! Tree shrews are small, arboreal animals native to the Old World. Long dumped in with the primates, new research suggests that they actually are distinct enough to make their own order, the Scandentia. Some tree shrew species are threatened, but others are common and likely to survive. The fact that they are allied to us, as well as the fact that they are adaptable and resemble the most primitive primates (i.e. Purgatorius) make them especially interesting.
This order you've definitely never heard of. Better known as "flying lemurs", colugos are an order with just two genera, both in Southeast Asia. However, they are also an ancient lineage, with possible colugo fossils (though incomplete) popping up in the Eocene. Colugos are strange creatures, distantly related to us, but having a patagium which they use to glide. Two other odd traits of colugos is that they are the best gliders of any mammal, and that they give birth almost like a marsupial, despite clearly being placentals. Colugos are herbivores. These bizzare animals need to be conserved, but luckily it doesn't seem like they are in as grave of a predicament as...say....the Javan Rhinoceros or the Giant Panda.
Once again, a truly awesome artiodactyl is overlooked on account of people wanting to see ferocious carnivorans, and massive rhinos, elephants, and giraffes. These lightweight antelopes have a particularly odd adaptation, one that gives them an advantage over their kin...their neck and legs. Gerenuks have immensely disproportionate necks and legs, which allow them to browse high above the other antelope of their region. They can even rear up and walk on their hind legs for short periods of time, which plays a part in their mating ritual. Gerenuks are interesting because they seem to have a lot of potential.
These are some of my favorite birds, specifically due to their weirdness. Hoatzin have the most untapped potential of almost any bird today. First off, as juveniles they have wing claws in an almost Archaeopteryx-like arrangement, allowing them to climb through the trees. These claws are lost on adulthood, but who knows what a little neotenous mutation could do. Secondly, hoatzin are the only birds that can ruminate, and along with geese are some of the only birds that can digest tough plant matter like grass (though hoatzin eat leaves). Their ruminating anatomy makes them poor fliers, so they hang around on branches a lot of the time. But, predators and people leave them alone, because as a side effect their rumination gives them an awful taste and smell. Thankfully, the hoatzin's fate is actually more assured than most other rainforest birds in South America, and will definitely survive for a while.
What looks like a crane, acts like a quail, but isn't either? The sunbittern. This odd little bird is so odd simply because it seems to be unrelated to anything. So far, the most likely idea is that this little bird is related to another odd species, the kagu of New Calidonia. There are some features which link these two together, like the prescence of powder down, but the jury is still out...and confused.
Desmans are aquatic relatives to the moles, looking all the world like shrews with paddles for feet. These small mammals are primarily insectovorous, though I would assume they would eat small fish if given the chance. What is interesting about these critters is that their limbs are almost exactly like those seen in the early whale Rodhocetus, which suggests that the latter animal swam like a desman. There appear to be many other interesting features of desmans, but unfortunately studies in desmans are lacking. Even worse, both species are threatened with extinction, and have little to no conservation effort underway to protect them.