The Formosan Clouded Leopard (Neofelis nebulosa brachyura) of Taiwan is now thought to be extinct. None have been seen in over thirty years, despite a recent and intensive 13-year effort to document one. We did just about everything we could to eliminate this animal; we destroyed their habitat, killed them for their skins, and got rid of the other animals they normally ate. They didn't have a chance.
The Cape Verde Giant Skink (Chioninia coctei), which hasn't been seen since 1912, has been declared extinct, although a jawbone from one of these lizards was found in some cat scat in 2005. However, since then the cat (i.e., house cat) population has increased substantially and, aided by rats and dogs, has likely wiped out the skink.
The Sri Lanka Spiny Eel (Macrognathus pentophthalmos) is probably extinct. As recently as 1980 the species was considered common but it was likely done in by a non-native species of fish that ate many of them.
The Eskimo Curlew (Numenius borealis) was once so abundant that the sizes of its flocks were compared to those of Passenger Pigeons. They now have something else in common. The last known Eskimo Curlew was observed in 1963; Canada is likely to decide it is officially extinct because it has been 50 years since one has been seen. Eskimo Curlews probably suffered from a decline in their locust prey as well as loss of habitat but the primary cause of extinction is thought to be overhunting. Indeed, the last known Eskimo Curlew was shot by a hunter in Barbados.